Weighted riesz bounded variation spaces and the nemytskii operator

David Cruz-Uribe; Oscar M. Guzmán; Humberto Rafeiro

Weighted riesz bounded variation spaces and the nemytskii operator

David Cruz-Uribe, Oscar M. Guzmán, Humberto Rafeiro

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We define a weighted version of the Riesz bounded variation space. We show that a generalization of the Riesz theorem relating these spaces to the Sobolev space W^1,p_pI_q holds for weighted Riesz bounded variation spaces when the weight belongs to the Muckenhoupt class. As an application, for weights belonging to the Muckenhoupt class, we characterize the globally Lipschitz Nemytskii operators acting in the weighted Riesz bounded variation spaces.

Original language	English
Pages (from-to)	125-139
Number of pages	15
Journal	Azerbaijan Journal of Mathematics
Volume	10
Issue number	2
Publication status	Published - 2020

Keywords

A weights
Banach function spaces
Nemytskii operators
Riesz bounded variation spaces
Variable Lebesgue spaces

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "We define a weighted version of the Riesz bounded variation space. We show that a generalization of the Riesz theorem relating these spaces to the Sobolev space W1,ppIq holds for weighted Riesz bounded variation spaces when the weight belongs to the Muckenhoupt class. As an application, for weights belonging to the Muckenhoupt class, we characterize the globally Lipschitz Nemytskii operators acting in the weighted Riesz bounded variation spaces.",

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AU - Guzmán, Oscar M.

AU - Rafeiro, Humberto

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N2 - We define a weighted version of the Riesz bounded variation space. We show that a generalization of the Riesz theorem relating these spaces to the Sobolev space W1,ppIq holds for weighted Riesz bounded variation spaces when the weight belongs to the Muckenhoupt class. As an application, for weights belonging to the Muckenhoupt class, we characterize the globally Lipschitz Nemytskii operators acting in the weighted Riesz bounded variation spaces.

AB - We define a weighted version of the Riesz bounded variation space. We show that a generalization of the Riesz theorem relating these spaces to the Sobolev space W1,ppIq holds for weighted Riesz bounded variation spaces when the weight belongs to the Muckenhoupt class. As an application, for weights belonging to the Muckenhoupt class, we characterize the globally Lipschitz Nemytskii operators acting in the weighted Riesz bounded variation spaces.

KW - A weights

KW - Banach function spaces

KW - Nemytskii operators

KW - Riesz bounded variation spaces

KW - Variable Lebesgue spaces

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IS - 2

ER -

Weighted riesz bounded variation spaces and the nemytskii operator

Abstract

Keywords

ASJC Scopus subject areas

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