Journal articles: 'Littlewood-Paley inequality'

1

Stevic, Stevo. "A Littlewood-Paley type inequality." Bulletin of the Brazilian Mathematical Society 34, no. 2 (July 1, 2003): 211–17. http://dx.doi.org/10.1007/s00574-003-0008-1.

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2

Wilson, J. M. "A semi-discrete Littlewood–Paley inequality." Studia Mathematica 153, no. 3 (2002): 207–33. http://dx.doi.org/10.4064/sm153-3-1.

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3

Djordjević, Olivera, and Miroslav Pavlović. "On a Littlewood-Paley type inequality." Proceedings of the American Mathematical Society 135, no. 11 (November 1, 2007): 3607–12. http://dx.doi.org/10.1090/s0002-9939-07-09016-8.

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4

Wilson, J. Michael. "Note on a Littlewood-Paley inequality." Proceedings of the American Mathematical Society 128, no. 12 (June 7, 2000): 3609–12. http://dx.doi.org/10.1090/s0002-9939-00-05504-0.

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5

Choa, Jun Soo, and Hong Oh Kim. "A Littlewood and Paley-type inequality on the ball." Bulletin of the Australian Mathematical Society 50, no. 2 (October 1994): 265–71. http://dx.doi.org/10.1017/s0004972700013721.

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6

Liu, Lanzhe. "Sharp endpoint inequality for multilinear Littlewood-Paley operator." Kodai Mathematical Journal 27, no. 2 (June 2004): 134–43. http://dx.doi.org/10.2996/kmj/1093351320.

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7

Prestini, Elena, and Per Sjölin. "A littlewood-paley inequality for the Carleson operator." Journal of Fourier Analysis and Applications 6, no. 5 (September 2000): 457–66. http://dx.doi.org/10.1007/bf02511540.

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8

SHIGEKAWA, Ichiro, and Nobuo YOSHIDA. "Littlewood-Paley-Stein inequality for a symmetric diffusion." Journal of the Mathematical Society of Japan 44, no. 2 (April 1992): 251–80. http://dx.doi.org/10.2969/jmsj/04420251.

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9

Pichorides, S. K. "A note on the Littlewood-Paley square function inequality." Colloquium Mathematicum 60, no. 2 (1990): 687–91. http://dx.doi.org/10.4064/cm-60-61-2-687-691.

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10

Borovitskiy, V. "Weighted Littlewood–Paley inequality for arbitrary rectangles in ℝ²." St. Petersburg Mathematical Journal 32, no. 6 (October 20, 2021): 975–97. http://dx.doi.org/10.1090/spmj/1680.

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Weighted counterparts of the one-sided Littlewood–Paley inequalities for arbitrary rectangles in R 2 \mathbb {R}^2 are proved. For a partition I \mathcal {I} of the plane R 2 \mathbb {R}^2 into rectangles with sides parallel to coordinate axes and a weight w ( ⋅ , ⋅ ) w(\,\cdot \,, \,\cdot \,) satisfying the two-parameter Muckenhoupt condition A p / 2 A_{p/2} for 2 > p > ∞ 2 > p > \infty , the following inequality holds: c p , w ‖ { M I f } I ∈ I ‖ L w p ( l 2 ) ≤ ‖ f ‖ L w p , \begin{equation*} c_{p, w}\lVert \{M_I f\}_{I \in \mathcal {I}} \rVert _{L^p_w(l^2)} \leq \lVert f \rVert _{L_w^p} , \end{equation*} where the symbols M I f ^ = f ^ χ I \widehat {M_I f} = \widehat {f} \chi _{I} denote the corresponding Fourier multipliers. For I \mathcal {I} as above, p p in the range 0 > p > 2 0 > p > 2 , and weights w w satisfying a dual condition α r ( p ) \alpha _{r(p)} , the following inequality holds ‖ ∑ I ∈ I f I ‖ L w p ≤ C p , w ‖ { f I } I ∈ I ‖ L w p ( l 2 ) , where supp ⁡ f I ^ ⊆ I for I ∈ I . \begin{equation*} \Big \|{\sum }_{I \in \mathcal {I}} f_I\Big \|_{L^p_w} \leq C_{p, w} \big \| \left \{ f_I \right \}_{I \in \mathcal {I}} \big \|_{L^p_w(l^2)} , \text { where } \operatorname {supp}{\widehat {f_I}} \subseteq I \text { for } I \in \mathcal {I}. \end{equation*} The proof is based on the theory of two-parameter singular integral operators on Hardy spaces developed by R. Fefferman and some of its more recent weighted generalizations. The former and the latter inequalities are extensions to the weighted setting, respectively, for Journe’s result of 1985 and Osipov’s result of 2010.

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11

Wang, Hua. "Morrey Spaces Related to Schrödinger Operators with Certain Nonnegative Potentials and Littlewood–Paley–Stein Functions on the Heisenberg groups." Studia Scientiarum Mathematicarum Hungarica 57, no. 4 (December 17, 2020): 465–507. http://dx.doi.org/10.1556/012.2020.57.4.1477.

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Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential V belongs to the reverse Hölder class with . Here is the homogeneous dimension of . Assume that is the heat semigroup generated by. The Lusin area integral and the Littlewood–Paley–Stein function associated with the Schrödinger operator are deﬁned, respectively, bywhereandWhere is a parameter. In this article, the author shows that there is a relationship between and the operator and for any , the following inequality holds true:Based on this inequality and known results for the Lusin area integral , the author establishes the strong-type and weak-type estimates for the Littlewood–Paley–Stein function on . In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator on . By using some pointwise estimates of the kernels related to the nonnegative potential V, the author establishes the boundedness properties of the operator acting on the Morrey spaces for an appropriate choice of . It can be shown that the same conclusions hold for the operator on generalized Morrey spaces as well.

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12

Pavlović, Miroslav. "A short proof of an inequality of Littlewood and Paley." Proceedings of the American Mathematical Society 134, no. 12 (June 15, 2006): 3625–27. http://dx.doi.org/10.1090/s0002-9939-06-08434-6.

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13

Luecking, Daniel H. "A new proof of an inequality of Littlewood and Paley." Proceedings of the American Mathematical Society 103, no. 3 (March 1, 1988): 887. http://dx.doi.org/10.1090/s0002-9939-1988-0947675-0.

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14

Pichorides, S. K. "A remark on the constants of the Littlewood-Paley inequality." Proceedings of the American Mathematical Society 114, no. 3 (March 1, 1992): 787. http://dx.doi.org/10.1090/s0002-9939-1992-1088445-6.

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15

Krylov, N. V. "A parabolic Littlewood-Paley inequality with applications to parabolic equations." Topological Methods in Nonlinear Analysis 4, no. 2 (December 1, 1994): 355. http://dx.doi.org/10.12775/tmna.1994.033.

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16

Osipov, N. N. "Littlewood–Paley–Rubio de Francia inequality for the Walsh system." St. Petersburg Mathematical Journal 28, no. 5 (July 25, 2017): 719–26. http://dx.doi.org/10.1090/spmj/1469.

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17

Potapov, Denis, Fedor Sukochev, and Quanhua Xu. "On the vector-valued Littlewood–Paley–Rubio de Francia inequality." Revista Matemática Iberoamericana 28, no. 3 (2012): 839–56. http://dx.doi.org/10.4171/rmi/693.

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18

Yoshida, N. "The Littlewood-Paley-Stein Inequality on an Infinite Dimensional Manifold." Journal of Functional Analysis 122, no. 2 (June 1994): 402–27. http://dx.doi.org/10.1006/jfan.1994.1074.

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19

Genchev, T. G. "A weighted version of the Paley–Wiener theorem." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 2 (March 1989): 389–95. http://dx.doi.org/10.1017/s0305004100067888.

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A generalization of the classical theorems of Paley and Wiener[5] and Plancherel and Polya[6] concerning entire functions of exponential type is obtained. The proof relies only on the Cauchy theorem and the Hardy–Littlewood inequality for the Fourier transform (see [8, 9]). Since the functions under consideration are supposed to be defined only in two opposite octants in ℂn, a version of the edge of the wedge theorem [7] is derived as a by-product.

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20

Osipov, N. N. "The Littlewood-Paley-Rubio de Francia inequality in Morrey-Campanato spaces." Sbornik: Mathematics 205, no. 7 (July 2014): 1004–23. http://dx.doi.org/10.1070/sm2014v205n07abeh004407.

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21

Magaril-Il’yaev, G. G., and K. Yu Osipenko. "Hardy-Littlewood-Paley inequality and recovery of derivatives from inaccurate data." Doklady Mathematics 83, no. 3 (June 2011): 337–39. http://dx.doi.org/10.1134/s1064562411030203.

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22

Sweezy, Caroline. "A Littlewood–Paley type inequality with applications to the elliptic Dirichlet problem." Annales Polonici Mathematici 90, no. 2 (2007): 105–30. http://dx.doi.org/10.4064/ap90-2-2.

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23

Soria, Fernando. "A Note on a Littlewood-Paley Inequality for Arbitrary Intervals in R2." Journal of the London Mathematical Society s2-36, no. 1 (August 1987): 137–42. http://dx.doi.org/10.1112/jlms/s2-36.1.137.

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24

Kislyakov, S. V., and D. V. Parilov. "On singular integrals related to the Littlewood-Paley inequality for arbitrary intervals." Journal of Mathematical Sciences 148, no. 6 (February 2008): 846–49. http://dx.doi.org/10.1007/s10958-008-0031-2.

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25

Osipov, N. N. "Littlewood–Paley–Rubio De Francia Inequality in Morrey–Campanato Spaces: An Announcement." Journal of Mathematical Sciences 202, no. 4 (September 23, 2014): 560–64. http://dx.doi.org/10.1007/s10958-014-2067-9.

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26

TRONG, NGUYEN NGOC, and LE XUAN TRUONG. "RIESZ TRANSFORMS AND LITTLEWOOD–PALEY SQUARE FUNCTION ASSOCIATED TO SCHRÖDINGER OPERATORS ON NEW WEIGHTED SPACES." Journal of the Australian Mathematical Society 105, no. 2 (June 18, 2018): 201–28. http://dx.doi.org/10.1017/s144678871700026x.

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Let ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+{\mathcal{V}}$ be a Schrödinger operator on $\mathbb{R}^{n},n\geq 3$, where ${\mathcal{V}}$ is a potential satisfying an appropriate reverse Hölder inequality. In this paper, we prove the boundedness of the Riesz transforms and the Littlewood–Paley square function associated with Schrödinger operators ${\mathcal{L}}$ in some new function spaces, such as new weighted Bounded Mean Oscillation (BMO) and weighted Lipschitz spaces, associated with ${\mathcal{L}}$. Our results extend certain well-known results.

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27

Chen, Yanping, and Wenyu Tao. "End Point Estimate of Littlewood-Paley Operator Associated to the Generalized Schrödinger Operator." Journal of Function Spaces 2021 (March 20, 2021): 1–8. http://dx.doi.org/10.1155/2021/8867966.

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Let L = − Δ + μ be the generalized Schrödinger operator on ℝ d , d ≥ 3 , where μ ≠ 0 is a nonnegative Radon measure satisfying certain scale-invariant Kato conditions and doubling conditions. In this work, we give a new BMO space associated to the generalized Schrödinger operator L , BM O θ , L , which is bigger than the BMO spaces related to the classical Schrödinger operators A = − Δ + V , with V a potential satisfying a reverse Hölder inequality introduced by Dziubański et al. in 2005. Besides, the boundedness of the Littlewood-Paley operators associated to L in BM O θ , L also be proved.

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28

Peláez, José Ángel, and Elena De la Rosa. "Littlewood–Paley inequalities for fractional derivative on Bergman spaces." Annales Fennici Mathematici 47, no. 2 (September 17, 2022): 1109–30. http://dx.doi.org/10.54330/afm.121831.

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For any pair $(n,p)$, $n\in\mathbb{N}$ and $0<p<\infty$, it has been recently proved by Peláez and Rättyä (2021) that a radial weight $\omega$ on the unit disc of the complex plane $\mathbb{D}$ satisfies the Littlewood-Paley equivalence $\int_{\mathbb{D}}|f(z)|^p\,\omega(z)\,dA(z)\asymp\int_\mathbb{D}|f^{(n)}(z)|^p(1-|z|)^{np}\omega(z)\,dA(z)+\sum_{j=0}^{n-1}|f^{(j)}(0)|^p,$ for any analytic function $f$ in $\mathbb{D}$, if and only if $\omega\in\mathcal{D}=\hat{\mathcal{D}} \cap \check{\mathcal{D}}$. A radial weight $\omega$ belongs to the class $\hat{\mathcal{D}}$ if $\sup_{0\le r<1} \frac{\int_r^1 \omega(s)\,ds}{\int_{\frac{1+r}{2}}^1\omega(s)\,ds}<\infty$, and $\omega \in \check{\mathcal{D}}$ if there exists $k>1$ such that $\inf_{0\le r<1} \frac{\int_{r}^1\omega(s)\,ds}{\int_{1-\frac{1-r}{k}}^1 \omega(s)\,ds}>1.$ In this paper we extend this result to the setting of fractional derivatives. Being precise, for an analytic function $f(z)=\sum_{n=0}^\infty \widehat{f}(n) z^n$ we consider the fractional derivative $D^{\mu}(f)(z)=\sum_{n=0}^{\infty} \frac{\widehat{f}(n)}{\mu_{2n+1}} z^n$ induced by a radial weight $\mu \in \mathcal{D}$ where $\mu_{2n+1}=\int_0^1 r^{2n+1}\mu(r)\,dr$. Then, we prove that for any $p\in (0,\infty)$, the Littlewood-Paley equivalence $\int_\mathbb{D} |f(z)|^p \omega(z)\,dA(z)\asymp \int_\mathbb{D}|D^{\mu}(f)(z)|^p\left[\int_{|z|}^1\mu(s)\,ds\right]^p\omega(z)\,dA(z)$holds for any analytic function $f$ in $\mathbb{D}$ if and only if $\omega\in\mathcal{D}$. We also prove that for any $p\in (0,\infty)$, the inequality $\int_\mathbb{D}|D^{\mu}(f)(z)|^p\left[\int_{|z|}^1\mu(s)\,ds\right]^p\omega(z)\,dA(z)\lesssim \int_\mathbb{D} |f(z)|^p \omega(z)\,dA(z)$ holds for any analytic function $f$ in $\mathbb D$ if and only if $\omega\in\hat D$.

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29

HONG, GUIXIANG. "Non-commutative ergodic averages of balls and spheres over Euclidean spaces." Ergodic Theory and Dynamical Systems 40, no. 2 (June 14, 2018): 418–36. http://dx.doi.org/10.1017/etds.2018.40.

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In this paper, we establish a non-commutative analogue of Calderón’s transference principle, which allows us to deduce the non-commutative maximal ergodic inequalities from the special case—operator-valued maximal inequalities. As applications, we deduce the non-commutative Stein–Calderón maximal ergodic inequality and the dimension-free estimates of the non-commutative Wiener maximal ergodic inequality over Euclidean spaces. We also show the corresponding individual ergodic theorems. To show Wiener’s pointwise ergodic theorem, following a somewhat standard way we construct a dense subset on which pointwise convergence holds. To show Jones’ pointwise ergodic theorem, we use again the transference principle together with the Littlewood–Paley method, which is different from Jones’ original variational method that is still unavailable in the non-commutative setting.

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30

Han, Jingqi, and Litan Yan. "Lp-Theory for the fractional time stochastic heat equation with an infinite-dimensional fractional Brownian motion." Infinite Dimensional Analysis, Quantum Probability and Related Topics 24, no. 02 (June 2021): 2150010. http://dx.doi.org/10.1142/s0219025721500107.

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In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.

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31

Auscher, P., and Ph Tchamitchian. "An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains." Publicacions Matemàtiques 43 (July 1, 1999): 685–711. http://dx.doi.org/10.5565/publmat_43299_09.

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32

Djordjevic, Olivera. "A Littlewood-Paley type inequality for harmonic functions in the unit ball of Rⁿ." Filomat 20, no. 2 (2006): 101–5. http://dx.doi.org/10.2298/fil0602105d.

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33

Osipov, N. N. "One-sided Littlewood–Paley inequality in $ {\mathbb{R}^n} $ for 0 < p ≤ 2." Journal of Mathematical Sciences 172, no. 2 (December 16, 2010): 229–42. http://dx.doi.org/10.1007/s10958-010-0195-4.

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34

Kim, Ildoo, and Kyeong-Hun Kim. "A generalization of the Littlewood–Paley inequality for the fractional Laplacian (−Δ)α/2." Journal of Mathematical Analysis and Applications 388, no. 1 (April 2012): 175–90. http://dx.doi.org/10.1016/j.jmaa.2011.11.031.

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35

MIZUTA, Yoshihiro, Eiichi NAKAI, Yoshihiro SAWANO, and Tetsu SHIMOMURA. "Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials." Journal of the Mathematical Society of Japan 65, no. 2 (April 2013): 633–70. http://dx.doi.org/10.2969/jmsj/06520633.

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36

Osipov, N. N. "Littlewood–Paley inequality for arbitrary rectangles in $\mathbb{R}^{2}$ for $0 < p \le2$." St. Petersburg Mathematical Journal 22, no. 2 (April 1, 2011): 293. http://dx.doi.org/10.1090/s1061-0022-2011-01141-0.

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37

Stolyarov, D. M. "New correction theorems in the light of a weighted Littlewood-Paley-Rubio de Francia inequality." Journal of Mathematical Sciences 182, no. 5 (April 6, 2012): 714–23. http://dx.doi.org/10.1007/s10958-012-0775-6.

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38

Cao, Mingming, Kangwei Li, and Qingying Xue. "A Characterization of Two-Weight Norm Inequality for Littlewood–Paley $$g_{\lambda }^{*}$$ g λ ∗ -Function." Journal of Geometric Analysis 28, no. 2 (April 20, 2017): 842–65. http://dx.doi.org/10.1007/s12220-017-9844-x.

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39

Kim, Ildoo, Kyeong-Hun Kim, and Panki Kim. "Parabolic Littlewood–Paley inequality forϕ(−Δ)-type operators and applications to stochastic integro-differential equations." Advances in Mathematics 249 (December 2013): 161–203. http://dx.doi.org/10.1016/j.aim.2013.09.008.

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40

Yang, Yinuo, Qingyan Wu, and Seong-Tae Jhang. "2D Linear Canonical Transforms on Lp and Applications." Fractal and Fractional 7, no. 2 (January 17, 2023): 100. http://dx.doi.org/10.3390/fractalfract7020100.

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As Fourier transformations of Lp functions are the mathematical basis of various applications, it is necessary to develop Lp theory for 2D-LCT before any further rigorous mathematical investigation of such transformations. In this paper, we study this Lp theory for 1≤p<∞. By defining an appropriate convolution, we obtain a result about the inverse of 2D-LCT on L1(R2). Together with the Plancherel identity and Hausdorff–Young inequality, we establish Lp(R2) multiplier theory and Littlewood–Paley theorems associated with the 2D-LCT. As applications, we demonstrate the recovery of the L1(R2) signal function by simulation. Moreover, we present a real-life application of such a theory of 2D-LCT by encrypting and decrypting real images.

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41

Tran, Tri Dung. "Musielak–Orlicz Hardy Spaces Associated with Divergence Form Elliptic Operators Without Weight Assumptions." Nagoya Mathematical Journal 216 (2014): 71–110. http://dx.doi.org/10.1215/00277630-2817420.

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AbstractLet L be a divergence form elliptic operator with complex bounded measurable coefficients, let ω be a positive Musielak-Orlicz function on (0, ∞) of uniformly strictly critical lower-type pω ∈ (0, 1], and let ρ(x,t) = t−1/ω−1 (x,t−1) for x ∈ ℝn, t ∊ (0, ∞). In this paper, we study the Musielak-Orlicz Hardy space Hω,L(ℝn) and its dual space BMOρ,L* (ℝ n), where L* denotes the adjoint operator of L in L2 (ℝ n). The ρ-Carleson measure characterization and the John-Nirenberg inequality for the space BMOρ,L (ℝn) are also established. Finally, as applications, we show that the Riesz transform ∇L−1/2 and the Littlewood–Paley g-function gL map Hω,L(ℝn) continuously into L(ω).

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42

Cao, Mingming, and Qingying Xue. "A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp -testing condition." Forum Mathematicum 30, no. 2 (March 1, 2018): 457–78. http://dx.doi.org/10.1515/forum-2017-0022.

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AbstractIn this paper, we present a local Tb theorem for the non-homogeneous Littlewood–Paley{g_{\lambda}^{*}}-function with non-convolution type kernels and upper power bound measure μ. Actually, we show that, under the assumptions{\operatorname{supp}b_{Q}\subset Q},{\lvert\int_{Q}b_{Q}\,d\mu|\gtrsim\mu(Q)}and{\|b_{Q}\|^{p}_{L^{p}(\mu)}\lesssim\mu(Q)}, the norm inequality{\|g_{\lambda}^{*}(f\/)\|_{L^{p}(\mu)}\lesssim\|f\/\|_{L^{p}(\mu)}}holds if and only if the following testing condition holds:\sup_{Q:\text{cubes in }\mathbb{R}^{n}}\frac{1}{\mu(Q)}\int_{Q}\Biggr{(}\int_{% 0}^{\ell(Q)}\int_{\mathbb{R}^{n}}\Bigl{(}\frac{t}{t+|x-y|}\Big{)}^{m\lambda}|% \theta_{t}(b_{Q})(y,t)|^{2}\frac{d\mu(y)\,dt}{t^{m+1}}\Bigg{)}^{p/2}d\mu(x)<\infty.This is the first time to investigate the{g_{\lambda}^{*}}-function in the simultaneous presence of three attributes: local, non-homogeneous and{L^{p}}-testing condition. It is important to note that the testing condition here is an{L^{p}}type with{p\in(1,2]}.

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43

Deng, Dongguo, and Dachun Yang. "Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type." Journal of the Australian Mathematical Society 80, no. 2 (April 2006): 229–62. http://dx.doi.org/10.1017/s1446788700013094.

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AbstractLet (X, ρ, μ)d, θ be a space of homogeneous type with d < 0 and θ ∈ (0, 1], b be a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0 ∈ (0, 1) be some constant depending on d, ∈ and s. The authors introduce the Besov space bBspq (X) with a0 > p ≧ ∞, and the Triebel-Lizorkin space bFspq (X) with a0 > p > ∞ and a0 > q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov space b−1 Bs (X) and the Triebel-Lizorkin space b−1 Fspq (X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems, T b theorems, and the lifting property by introducing some new Riesz operators of these spaces.

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44

Kim, Ildoo, Kyeong-Hun Kim, and Sungbin Lim. "Parabolic Littlewood–Paley inequality for a class of time-dependent pseudo-differential operators of arbitrary order, and applications to high-order stochastic PDE." Journal of Mathematical Analysis and Applications 436, no. 2 (April 2016): 1023–47. http://dx.doi.org/10.1016/j.jmaa.2015.12.040.

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45

Rubio de Francia, José. "A Littlewood-Paley Inequality for Arbitrary Intervals." Revista Matemática Iberoamericana, 1985, 1–14. http://dx.doi.org/10.4171/rmi/7.

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46

Tselishchev, Anton Sergeevich. "Littlewood-Paley-Rubio de Francia inequality for bounded Vilenkin systems." Sbornik: Mathematics 212, no. 10 (2021). http://dx.doi.org/10.1070/sm9482.

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47

Ben Salem, Néjib. "Hardy–Littlewood–Sobolev-Type Inequality for the Fractional Littlewood–Paley g-Function in Jacobi Analysis." Bulletin of the Malaysian Mathematical Sciences Society, September 3, 2021. http://dx.doi.org/10.1007/s40840-021-01181-0.

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48

Borovitskiy, V. "Littlewood–Paley–Rubio De Francia Inequality for the Two-Parameter Walsh System." Journal of Mathematical Sciences, April 6, 2022. http://dx.doi.org/10.1007/s10958-022-05785-0.

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49

Akgün, R. "Jackson type inequalities for differentiable functions in weighted Orlicz spaces." St. Petersburg Mathematical Journal, December 16, 2022. http://dx.doi.org/10.1090/spmj/1743.

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In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt A p A_p condition. To obtain a refined version of the Jackson type inequality, an extrapolation theorem, Marcinkiewicz multiplier theorem, and Littlewood–Paley type results are proved. As a consequence, refined inverse Marchaud type inequalities are obtained. By means of a realization result, an equivalence is found between the fractional order weighted modulus of smoothness and Peetre’s classical weighted K K -functional.

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50

Tselishchev, A. "On a Vector-Valued Extension of the Littlewood–Paley–Rubio De Francia Inequality for Walsh Functions." Journal of Mathematical Sciences, December 3, 2022. http://dx.doi.org/10.1007/s10958-022-06223-x.

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Journal articles on the topic 'Littlewood-Paley inequality'

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