论文标题
各向异性强壮空间的分子分解，并具有可变指数
Molecular Decomposition of Anisotropic Hardy Spaces with Variable Exponents
论文作者
论文摘要
令$ a $成为$ \ m athbb {r}^n $和$ p（\ cdot）上的广泛扩张：\ mathbb {r}^n \ rightArow（0，\，\ infty）$是满足全球log-hölder连续状态的变量指数函数。令$ h^{p（\ cdot）} _ a（{\ mathbb {r}}^n）$为变量各向异性耐寒空间，通过非区别的大最大函数定义。在本文中，作者建立了其分子分解，即使在经典的各向同性设置中，它仍然是新的（在情况下，$ a：= 2 \ mathrm i_ {n \ times n} $）。作为应用程序，作者从$ h^{p（\ cdot）} _ {a}（\ Mathbb {r}^n）$ to $ h^{ $ h^{p（\ cdot）} _ {a}（\ mathbb {r}^n）$本身。
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.
