论文标题
可变各向异性耐寒空间的分子表征，并应用于Calderón-Zygmund操作员的界面
Molecular Characterizations of Variable Anisotropic Hardy Spaces with Applications to Boundedness of Calderón-Zygmund Operators
论文作者
论文摘要
令$ p（\ cdot）：\ \ mathbb {r}^n \ to（0，\ infty] $是可变的指数函数，可满足全球log-hölder连续状态，$ a $ a $ a $ a a $ \ \ \ \ mathbb {rathbb {r}^n $。与$ a $ A $相关的各向异性耐受性空间在本文中通过非区别的大最大功能定义。 $ h_a^{p（\ cdot）}（\ mathbb {r}^n）$上的运算符，用于证明$ h_a^{p（\ cdot）}（\ cdot）}（\ mathbb {\ mathbb {r} n）$ and and and and and and and and and and and。 $ H_A^{p（\ cdot）}（\ Mathbb {r}^n）$从变量lebesgue space $ l^{p（\ cdot）}（\ mathbb {r}^n）$都列出了所有这些结果。
Let $p(\cdot):\ \mathbb{R}^n\to(0,\infty]$ be a variable exponent function satisfying the globally log-Hölder continuous condition and $A$ a general expansive matrix on $\mathbb{R}^n$. Let $H_A^{p(\cdot)}(\mathbb{R}^n)$ be the variable anisotropic Hardy space associated with $A$ defined via the non-tangential grand maximal function. In this article, via the known atomic characterization of $H_A^{p(\cdot)}(\mathbb{R}^n)$, the author establishes its molecular characterization with the known best possible decay of molecules. As an application, the author obtains a criterion on the boundedness of linear operators on $H_A^{p(\cdot)}(\mathbb{R}^n)$, which is used to prove the boundedness of anisotropic Calderón-Zygmund operators on $H_A^{p(\cdot)}(\mathbb{R}^n)$. In addition, the boundedness of anisotropic Calderón-Zygmund operators from $H_A^{p(\cdot)}(\mathbb{R}^n)$ to the variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^n)$ is also presented. All these results are new even in the classical isotropic setting.
