Bilinear Calderón-Zygmund operators on products of variable Hardy spaces
type: Item
instance of: scholarly article
title: Bilinear Calderón-Zygmund operators on products of variable Hardy spaces
zbMATH Open document ID: 1414.42017
author: Jian Tan
published in: Forum Mathematicum
publication date: 2019-03-20T00:00:00Z
review text: Let $p:\mathbb{R}^n\to (0, \infty]$ be a measurable function. Then the variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^n)$ consists of all Lebesgue measurable functions $f$ satisfying \[ \int_{\mathbb{R}^n}|\epsilon f(x)|^{p(x)}\,dx<\infty \] for some $\epsilon\in(0,\infty)$. Moreover, for any $f\in L^{p(\cdot)}(\mathbb{R}^n)$, let \[ \|f\|_{L^{p(\cdot)}(\mathbb{R}^n)}:=\inf\left\{\lambda>0: \int_{\mathbb{R}^n} \left(\frac{|f(x)|}{\lambda}\right)^{p(x)}\,dx\le 1\right\}. \] In this paper, under some assumptions for the function $p(\cdot)$, the author obtains the boundedness of bilinear Calderón-Zygmund operators from products of variable Hardy spaces into variable Lebesgue spaces or variable Hardy spaces.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 7039548
zbMATH Keywords: bilinear Calderón-Zygmund operators
zbMATH Keywords: variable exponent
zbMATH Keywords: atomic decomposition
zbMATH Keywords: Hardy space
reviewed by: Sibei Yang
MaRDI profile type: Publication
full work available at URL: forum-2018-0082
OpenAlex ID: W2891874312
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DOI: 10.1515/FORUM-2018-0082
description: scientific article; zbMATH DE number 7039548