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Research Article | Open Access

Weak Hardy spaces associated with para-accretive functions and their applications

Yan Wang1( ), Xintian Dong2, Fanghui Liao2
School of Science, China University of Mining and Technology, Beijing 100083, China
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
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Abstract

In this paper, we introduced a new class of weak Hardy spaces, denoted by Hbp,∞, and provided an analysis of their atomic decomposition. As an application, we established the boundedness of Calderón-Zygmund operators (CZOs) from Hp to Hbp,∞ including cases at the critical exponent

p=nn+δ,

where δ represents the regularity index of the distributional kernel. Moreover, the boundedness of CZOs from Hp,∞ to Hbp,∞ was demonstrated for

nn+δ<p≤1.

Keywords

weak Hardy spacepara-accretive functionatomic decompositionCalderón-Zygmund operator
CLC number: 42B20, 42B25, 42B35

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 30572-30596
DOI: 10.3934/math.20241476

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Cite this article:
Wang Y, Dong X, Liao F. Weak Hardy spaces associated with para-accretive functions and their applications. AIMS Mathematics, 2024, 9(11): 30572-30596. https://doi.org/10.3934/math.20241476

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Received: 07 August 2024
Revised: 11 October 2024
Accepted: 16 October 2024
Published: 28 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)