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July 2020 Calderón-Zygmund operators with variable kernels acting on weak Musielak-Orlicz Hardy spaces
Bo Li
Hiroshima Math. J. 50(2): 151-168 (July 2020). DOI: 10.32917/hmj/1595901624


Abstract. Let $\varphi : \mathbb R^n \times [0,\infty) \rightarrow [0,\infty)$ satisfy that $\varphi(x,\cdot)$ is an Orlicz function for any given $x \in \mathbb R^n$, and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty$ weight uniformly in $t \in (0,\infty)$. The weak Musielak-Orlicz Hardy space $WH^\varphi(\mathbb R^n)$ is defined to be the set of all tempered distributions such that their grand maximal functions belong to the weak Musielak-Orlicz space $WL^\varphi(\mathbb R^n)$. In this paper, we discuss the boundedness of the Calderón-Zygmund operator with variable kernel from $WH^\varphi(\mathbb R^n)$ to $WL^\varphi(\mathbb R^n)$. These results are new even for the classical weighted weak Hardy space and probably new for the classical weak Hardy space.


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Bo Li. "Calderón-Zygmund operators with variable kernels acting on weak Musielak-Orlicz Hardy spaces." Hiroshima Math. J. 50 (2) 151 - 168, July 2020.


Received: 3 May 2018; Revised: 7 February 2020; Published: July 2020
First available in Project Euclid: 28 July 2020

zbMATH: 07256501
MathSciNet: MR4132585
Digital Object Identifier: 10.32917/hmj/1595901624

Primary: 42B20
Secondary: 42B30 , 46E30

Keywords: Calderón-Zygmund operator , Muckenhoupt weight , Musielak-Orlicz function , variable kernel , weak Hardy space

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

Vol.50 • No. 2 • July 2020
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