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Aiting Wang

Publications and source records attributed to Aiting Wang.

6 recordsLinked to original sources
arXiv2025

Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors obtain the boundedness of certain sublinear operators from $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, where $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ denotes the Herz-type space associated with ball quasi-Banach function space $X$. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces.

math.FA↗
arXiv2022

The Fourier Transform of Anisotropic Hardy Spaces with Variable Exponents and Their Applications

Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-Hölder continuous condition. Let $\mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors obtain that the Fourier transform of $f\in \mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ coincides with a continuous function $F$ on $\mathbb{R}^n$ in the sense of tempered distributions. As applications, the authors further conclude a higher order convergence of the continuous function $F$ at the origin and then give a variant of the Hardy-Littlewood inequality in the setting of anisotropic Hardy spaces with variable exponents.

math.CA↗
arXiv2022

The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\mathbb{R}^n$ by Atoms and Molecules

Let $\vec{p}\in(0,\,\infty)^n$, $A$ be an expansive dilation on $\mathbb{R}^n$,and $H^{\vec{p}}_A({\mathbb {R}}^n)$ be the anisotropic mixed-norm Hardy space defined via the non-tangential grand maximal function studied by \cite{hlyy20}. In this paper, the authors establish new atomic and molecular decompositions of $H^{\vec{p}}_A({\mathbb {R}}^n)$. As an application, the authors obtain a boundedness criterion for a class of linear operators from $H^{\vec{p}}_{A}(\mathbb{R}^n)$ to $H^{\vec{p}}_{A}(\mathbb{R}^n)$. Part of results are still new even in the classical isotropic setting (in the case $A:=2\mathrm I_{n\times n}$, ${\mathrm{I}}_{n\times n}$ denotes the $n\times n$ unit matrix).

math.FA↗
arXiv2021

Maximal Function Characterizations of Hardy Spaces on ${\mathbb{R}}^{n}$ with Pointwise Variable Anisotropy

In 2011, Dekel et al. developed highly geometric Hardy spaces $H^p(Θ)$, for the full range $0<p\leq 1$, which are constructed by continuous multi-level ellipsoid covers $Θ$ of $\mathbb{R}^n$ with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. In this article, if the cover $Θ$ is pointwise continuous, then the authors further obtain some real-variable characterizations of $H^p(Θ)$ in terms of the radial, the non-tangential and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

math.FA↗
arXiv2020

Molecular Decomposition of Anisotropic Hardy Spaces with Variable Exponents

Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-Hölder continuous condition. Let $H^{p(\cdot)}_A({\mathbb {R}}^n)$ be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors establish its molecular decomposition, which is still new even in the classical isotropic setting (in the case $A:=2\mathrm I_{n\times n}$). As applications, the authors obtain the boundedness of anisotropic Calderón-Zygmund operators from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to $L^{p(\cdot)}(\mathbb{R}^n)$ or from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to itself.

math.CA↗