可变Lebesgue空间上双线性极大算子的加权范数不等式

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-11-01 DOI:10.5565/publmat6422004

D. Cruz-Uribe, O. Guzmán

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引用次数: 3

摘要

我们将变Lebesgue空间上的加权范数不等式理论推广到双线性算子的情况。我们引入了变量$\a_\pp$条件的双线性形式，并证明了双线性极大算子满足加权范数不等式的充要条件。我们的工作推广了第一作者Fiorenza和Neugebauer\cite{dcu-f-nPreprint2010}在可变Lebesgue空间中的线性结果以及Lerner等人在经典Lebesgue空格中的双线性结果。作为一个应用，我们证明了变Lebesgue空间中双线性奇异积分算子的加权范数不等式。

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Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces

We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators. We introduce a bilinear version of the variable $\A_\pp$ condition, and show that it is necessary and sufficient for the bilinear maximal operator to satisfy a weighted norm inequality. Our work generalizes the linear results of the first author, Fiorenza and Neugebauer \cite{dcu-f-nPreprint2010} in the variable Lebesgue spaces and the bilinear results of Lerner {\em et al.} \cite{MR2483720} in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.