Atomic and maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type
Atomic and maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type
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与齐次类型空间上的非负自伴随算子相关的 Musielak-Orlicz-Hardy 空间的原子函数和极大函数表征
DOI：
10.1007/s13348-019-00237-6
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发表时间：
2019
影响因子：
1.1
通讯作者：
Yang Dachun
中科院分区：
文献类型：
--
作者：
Yang Sibei;Yang Dachun
设一个具有倍测度的度量空间和一个热核满足高斯上界估计的非负自伴随算子。假设生长函数满足Orlicz函数和（一致Muckenhoupt权重的类）。让通过与l的热半群相关的Lusin面积函数定义的Musielak-Orlicz-Hardy空间。在本文中，作者用原子、非切向和径向极大函数来表征空间。特别是当，得到了局部非切向和径向极大函数的刻画。作为应用，作者在Dirichlet和Neumann边界条件下，得到了二阶自伴随椭圆算子在强Lipschitz域上的“几何”Musielak-Orlicz-Hardy空间的各种极大函数和原子特征；即使在任何情况下，本文给出的等效描述通过消除无界假设来改进已知结果。
Letbe a metric space with doubling measure andLbe a non-negative self-adjoint operator onwhose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth functionsatisfies thatis an Orlicz function and(the class of uniformly Muckenhoupt weights). Letbe the Musielak–Orlicz–Hardy space defined via the Lusin area function associated with the heat semigroup ofL. In this article, the authors characterize the spaceby means of atoms, non-tangential and radial maximal functions associated withL. In particular, when, the local non-tangential and radial maximal function characterizations ofare obtained. As applications, the authors obtain various maximal function and the atomic characterizations of the “geometric” Musielak–Orlicz–Hardy spacesandon the strongly Lipschitz domaininassociated with second-order self-adjoint elliptic operators with the Dirichlet and the Neumann boundary conditions; even whenfor anyand, the equivalent characterizations ofgiven in this article improve the known results via removing the assumption thatis unbounded.