论文标题
最大功能和Riesz转换与均匀高阶椭圆算子和球准散型函数空间相关的强大空间的特征
Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces
论文作者
论文摘要
令$ l $为均质的差异椭圆运算符，具有复杂有限的可测量系数，可在$ \ mathbb {r}^n $和$ x $ a Ball Quasi-Banach功能空间上$ \ Mathbb {r}^n $满足一些轻度假设。用$ h_ {x，\，l}表示（\ mathbb {r}^n）$与$ l $和$ x $相关的hardy空间，这是通过lusin区域函数定义的，该功能与$ l $生成的semigroup相关。在本文中，作者同时建立了$ h_ {x，\，l}（\ mathbb {r}^n）$的最大函数和riesz变换特征。本文中获得的结果具有广泛的一般性，可以应用于加权的耐寒空间，可变的耐寒空间，混合空间的空间，orlicz- hardy空间，orlicz-slice hardy空间以及与$ l $相关的莫雷（Morrey-Hardy）空间。特别是，即使$ l $是椭圆形算子的二阶差异，最大函数和Riesz变换了混合型硬质空间的特征，Orlicz-slice Hardy空间以及与本文获得的$ L $相关的莫雷 - hardy空间，与$ L $相关的空间都是全新的。
Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by $H_{X,\, L}(\mathbb{R}^n)$ the Hardy space, associated with both $L$ and $X$, which is defined via the Lusin area function related to the semigroup generated by $L$. In this article, the authors establish both the maximal function and the Riesz transform characterizations of $H_{X,\, L}(\mathbb{R}^n)$. The results obtained in this article have a wide range of generality and can be applied to the weighted Hardy space, the variable Hardy space, the mixed-norm Hardy space, the Orlicz--Hardy space, the Orlicz-slice Hardy space, and the Morrey--Hardy space, associated with $L$. In particular, even when $L$ is a second order divergence form elliptic operator, both the maximal function and the Riesz transform characterizations of the mixed-norm Hardy space, the Orlicz-slice Hardy space, and the Morrey--Hardy space, associated with $L$, obtained in this article, are totally new.
