Riesz Transform Characterization of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces [PDF]
arXiv, 2022 Let $X$ be a ball quasi-Banach function space satisfying some mild assumptions and $H_X(\mathbb{R}^n)$ the Hardy space associated with $X$. In this article, the authors introduce both the Hardy space $H_X(\mathbb{R}^{n+1}_+)$ of harmonic functions and the Hardy space $\mathbb{H}_X(\mathbb{R}^{n+1}_+)$ of harmonic vectors, associated with $X$, and then ...
arxiv
Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces [PDF]
arXiv, 2022 Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by $H_{X,\, L}(\mathbb{R}^n)$ the Hardy space, associated with both $L$ and $X$, which is defined via the Lusin area ...
arxiv
Hardy-Littlewood-type theorems for Fourier transforms in $\R^d$ [PDF]
arXiv, 2022 We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1
arxiv
Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds [PDF]
arXiv, 2021 We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy inequalities. These Hardy inequalities are in the spirit of Brezis-V\'{a}zquez in the Euclidean spaces.
arxiv
Real-Variable Theory of Local Variable Hardy Spaces [PDF]
arXiv, 2021 In this paper, we give a complete real-variable theory of local variable Hardy spaces. First, we present various real-variable characterizations in terms of several local maximal functions. Next, the new atomic and the finite atomic decomposition for the local variable Hardy spaces are established.
arxiv
Contractive multipliers from Hardy space to weighted Hardy space [PDF]
arXiv, 2012 It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied to get results on interpolation for a Hardy-to-weighted-Hardy contractive multiplier class.
arxiv
Composition operators on Hardy-Sobolev spaces and $BMO$-quasiconformal mappings [PDF]
arXiv, 2021 In this paper we consider composition operators on Hardy-Sobolev spaces in connections with $BMO$-quasiconformal mappings. Using the duality of Hardy spaces and $BMO$-spaces we prove that $BMO$-quasiconformal mappings generate bounded composition operators from Hardy-Sobolev spaces to Sobolev spaces.
arxiv
Parameterized Littlewood-Paley operators with variable kernels on Hardy spaces and weak Hardy spaces [PDF]
arXiv, 2017 In this paper, by using the atomic decomposition theory of Hardy space and weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley operator with variable kernel on these spaces.
arxiv
Weighted local Hardy spaces and their applications [PDF]
arXiv, 2010 In this paper, we study weighted local Hardy spaces $h^p_\wz(\rz)$ associated with local weights which include the classical Muckenhoupt weights. This setting includes the classical local Hardy space theory of Goldberg \cite{g}, and the weighted Hardy spaces of Bui \cite{bu}.
arxiv