The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\mathbb{R}^n$ by Atoms and Molecules
Abstract
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).
- Publication:
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arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.07611
- arXiv:
- arXiv:2203.07611
- Bibcode:
- 2022arXiv220307611W
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Classical Analysis and ODEs;
- Primary 42B20;
- Secondary 42B30;
- 46E30
- E-Print:
- 21