Maximal function characterizations of Hardy spaces associated with both non-negative self-adjoint operators satisfying Gaussian estimates and ball quasi-Banach function spaces

IF 1.2 4区数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-03-01 DOI:10.1007/s10473-024-0207-y

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Abstract

Assume that L is a non-negative self-adjoint operator on L²(ℝⁿ) with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space on ℝⁿ satisfying some mild assumptions. Let H_{X, L}(ℝⁿ) 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(ℝⁿ) 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.

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与满足高斯估计的非负自兼算子和球准巴纳赫函数空间相关的哈代空间的最大函数特征

摘要假设 L 是 L2(ℝn) 上的非负自相加算子，其热核满足所谓的高斯上界估计；X 是 ℝn 上的球准巴纳赫函数空间，满足一些温和的假设。让 HX, L(ℝn) 成为与 X 和 L 相关联的哈代空间，它由与 L 生成的半群相关的 Lusin 面积函数定义。在这篇文章中，作者建立了哈代空间 HX,L(ℝn) 的各种最大函数特征，然后应用这些特征获得了相关考西问题的可解性。这些结果具有广泛的通用性，特别是，这些结果可应用于的特定空间 X 包括加权空间、变量空间、混合规范空间、奥利奇空间、奥利奇切片空间和莫雷空间。此外，所获得的与 L 相关的混合规范哈代空间、奥利奇-切片哈代空间和莫雷-哈代空间的最大函数特征也是全新的。

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.