Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces
Cruz-Uribe, David (University of Alabama. Department of Mathematics)
Guzmán, O. M. (Universidad Nacional de Colombia. Departamento de Matemáticas)

Date:	2020
Abstract:	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 Ap(·) 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 [7] in the variable Lebesgue spaces and the bilinear results of Lerner et al. [22] in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.
Note:	The first author is supported by research funds from the Dean of the College of Arts & Sciences, the University of Alabama.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Publicacions matemàtiques, Vol. 64 Núm. 2 (2020) , p. 453-498 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/371191
DOI: 10.5565/PUBLMAT6422004

46 p, 523.2 KB

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