MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Xiaosheng LIN; Dachun YANG; Sibei YANG; Wen YUAN

doi:10.1007/s10473-024-0207-y

2024 , Vol. 44 >Issue 2: 484 - 514

DOI: https://doi.org/10.1007/s10473-024-0207-y

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Xiaosheng LIN ,
Dachun YANG ,
Sibei YANG ,
Wen YUAN

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1. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
2. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China;
3. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Xiaosheng LIN, E-mail: xslin@mail.bnu.edu.cn; Sibei YANG, E-mail: yangsb@lzu.edu.cn; Wen YUAN, E-mail: wenyuan@bnu.edu.cn

Received date: 2022-12-02

Revised date: 2023-10-15

Online published: 2024-04-16

Supported by

National Key Research and Development Program of China (2020YFA0712900), the National Natural Science Foundation of China (12371093, 12071197, 12122102 and 12071431), the Key Project of Gansu Provincial National Science Foundation (23JRRA1022), the Fundamental Research Funds for the Central Universities (2233300008 and lzujbky-2021-ey18) and the Innovative Groups of Basic Research in Gansu Province (22JR5RA391).

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Abstract

Assume that $L$ is a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ with its heat kernels satisfying the so-called Gaussian upper bound estimate and that $X$ is a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Let $H_{X,\,L}(\mathbb{R}^n)$ be the Hardy space associated with both $X$ and $L,$ which is defined by the Lusin area function related to the semigroup generated by $L$. In this article, the authors establish various maximal function characterizations of the Hardy space $H_{X,\,L}(\mathbb{R}^n)$ and then apply these characterizations to obtain the solvability of the related Cauchy problem. These results have a wide range of generality and, in particular, the specific spaces $X$ to which these results can be applied include the weighted space, the variable space, the mixed-norm space, the Orlicz space, the Orlicz-slice space, and the Morrey space. Moreover, the obtained maximal function characterizations of the mixed-norm Hardy space, the Orlicz-slice Hardy space, and the Morrey-Hardy space associated with $L$ are completely new.

Key words： Hardy space; ball quasi-Banach function space; Gaussian upper bound estimate; non-negative self-adjoint operator; maximal function

Cite this article

Xiaosheng LIN , Dachun YANG , Sibei YANG , Wen YUAN . MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES[J]. Acta mathematica scientia, Series B, 2024 , 44(2) : 484 -514 . DOI: 10.1007/s10473-024-0207-y

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