2,597 Citations
Bounds of Singular Integrals on Weighted Hardy Spaces and Discrete Littlewood–Paley Analysis
- Mathematics
- 2012
We apply the discrete version of Calderón’s reproducing formula and Littlewood–Paley theory with weights to establish the $H^{p}_{w} \to H^{p}_{w}$ (0<p<∞) and $H^{p}_{w}\to L^{p}_{w}$ (0<p≤1)…
Boundedness of Singular Integrals on Multiparameter Weighted Hardy Spaces $\text{{\textit{H}}}^\text{{\textit{p}}}_{\text{{\textit{w}}}}\ (\mathbb{R}^{\text{{\textit{n}}}}\times \mathbb{R}^{\text{{\textit{m}}}})$
- Mathematics
- 2012
We apply the discrete version of Calderón’s identity and Littlewood–Paley–Stein theory with weights to derive the $(H^p_w, H^p_w)$ and $(H^p_w, L^p_w) (0<p\le 1)$ boundedness for multiparameter…
New Ball Campanato-Type Function Spaces and Their Applications
- MathematicsThe Journal of Geometric Analysis
- 2022
Let X be a ball quasi-Banach function space on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…
Riesz Transform Characterization of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
- Mathematics
- 2022
Let X be a ball quasi-Banach function space satisfying some mild assumptions and H X ( R n ) the Hardy space associated with X . In this article, the authors introduce both the Hardy space H X ( R n…
Necessary and sufficient conditions for boundedness of commutators associated with Calderón–Zygmund operators on slice spaces
- Materials ScienceAnnals of Functional Analysis
- 2022
Let t∈(0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces
- Mathematics
- 2022
Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on R and X a ball quasi-Banach function space on R satisfying some mild assumptions.…
Boundedness of Fractional Integrals on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
- Mathematics
- 2022
Let X be a ball quasi-Banach function space on R n and H X ( R n ) the Hardy space associated with X , and let α ∈ (0 , n ) and β ∈ (1 , ∞ ). In this article, assuming that the (pow-ered)…
Commutators of Hausdorff operators on Herz-type Hardy spaces
- MathematicsAdvances in Operator Theory
- 2022
In this article, by applying the results of Zhou (Taiwan J Math 13:983–996, 2009), we investigate the boundedness for the commutators of Hausdorff operators on the weighted Herz-type Hardy spaces…
The CMO-Dirichlet Problem for the Schrödinger Equation in the Upper Half-Space and Characterizations of CMO
- MathematicsThe Journal of Geometric Analysis
- 2022
Let L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
Fourier Transform of Anisotropic Mixed-norm Hardy Spaces with Applications to Hardy-Littlewood Inequalities
- Mathematics
- 2021
. Let (cid:126)p ∈ (0 , 1] n be an n -dimensional vector and A a dilation. Let H (cid:126)pA ( R n ) denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the…
References
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Generalization of the Cauchy-Riemann Equations and Representations of the Rotation Group
- Mathematics
- 1968
On the existence of certain singular integrals
- Mathematics
- 1952
Let f (x) and K (x) be two functions integrable over the interval (-∞,+∞). It is very well known that their composition
$$ \int\limits_{{ - \infty }}^{{ + \infty }} {f(t)K\left( {x - t} \right)dt}…