论文标题
Riesz转换与Ball Quasi-Banach功能空间相关的耐铁空间的表征
Riesz Transform Characterization of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
论文作者
论文摘要
令$ x $为一个球式式式功能空间，满足一些温和的假设和$ h_x（\ mathbb {r}^n）$与$ x $相关的hardy空间。在本文中，作者介绍了谐波函数的hardy空间$ h_x（\ mathbb {r}^{n+1} _+）$，也是hardy space $ \ mathbb {h} _x（\ mathbb {r} $ h_x（\ MATHBB {r}^n）$，$ h_ {x，2}（\ Mathbb {r}^{n+1} _+）$和$ \ m athbb {h} _ {x _ {x，2} $ h_ {x，2}（\ Mathbb {r}^{n+1} _+）$和$ \ Mathbb {h} _ {x，2}（\ Mathbb {r}^{n+1} _+1} _+）是$ h_x（n+1} _ $ \ mathbb {h} _x（\ mathbb {r}^{n+1} _+）$。使用这些同构，作者建立了$ H_X（\ Mathbb {r}^n）$的第一阶Riesz变换特征。还获得了$ H_X（\ Mathbb {r}^n）$的高级Riesz变换特征。本文获得的结果具有广泛的一般性，可以应用于经典的耐寒空间，加权耐寒的空间，Herz-Hardy空间，Lorentz-Hardy空间，可变的Hardy空间，混合NORM HARTY空间，局部广义的Herz-Hardy Space和Mixper-Norm-Norm Herz-Herz-Hardy Space。
Let $X$ be a ball quasi-Banach function space satisfying some mild assumptions and $H_X(\mathbb{R}^n)$ the Hardy space associated with $X$. In this article, the authors introduce both the Hardy space $H_X(\mathbb{R}^{n+1}_+)$ of harmonic functions and the Hardy space $\mathbb{H}_X(\mathbb{R}^{n+1}_+)$ of harmonic vectors, associated with $X$, and then establish the isomorphisms among $H_X(\mathbb{R}^n)$, $H_{X,2}(\mathbb{R}^{n+1}_+)$, and $\mathbb{H}_{X,2}(\mathbb{R}^{n+1}_+)$, where $H_{X,2}(\mathbb{R}^{n+1}_+)$ and $\mathbb{H}_{X,2}(\mathbb{R}^{n+1}_+)$ are, respectively, certain subspaces of $H_X(\mathbb{R}^{n+1}_+)$ and $\mathbb{H}_X(\mathbb{R}^{n+1}_+)$. Using these isomorphisms, the authors establish the first order Riesz transform characterization of $H_X(\mathbb{R}^n)$. The higher order Riesz transform characterization of $H_X(\mathbb{R}^n)$ is also obtained. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz-Hardy space, the Lorentz-Hardy space, the variable Hardy space, the mixed-norm Hardy space, the local generalized Herz-Hardy space, and the mixed-norm Herz-Hardy space.
