论文标题
各向异性混合 - 耐用空间的特征在$ \ mathbb {r}^n $由原子和分子的
The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\mathbb{R}^n$ by Atoms and Molecules
论文作者
论文摘要
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 \ cite {hlyy20}研究的最大函数。在本文中，作者建立了$ h^{\ vec {p}}} _ a（{\ Mathbb {r}}^n）$的新的原子和分子分解。作为一个应用程序，作者从$ h^{\ vec {p}} _ {a}（\ Mathbb {r}^n）$ to $ h^{\ vec {r}^n）$ to $ h^{\ h^{\ vec {p}}} _}（\ vec {p}} _ {a} a}（\ mathbbbb {r Mathbb {r} n）$。即使在经典的各向同性设置中，结果的一部分仍然是新的（在情况下$ a：= 2 \ mathrm i_ {n \ times n} $，$ {\ mathrm {i}} _ {n \ times n} $表示$ n \ times n $ n $单位矩阵）。
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).
