A characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces

David Cruz-Uribe; Oscar Guzmán; Humberto Rafeiro

doi:10.4064/sm230729-14-12

A characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces

David Cruz-Uribe, Oscar Guzmán, Humberto Rafeiro

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

We introduce weighted Riesz bounded variation spaces defined on an open subset of n-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia’s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.

Original language	English
Pages (from-to)	287-304
Number of pages	18
Journal	Studia Mathematica
Volume	274
Issue number	3
DOIs	https://doi.org/10.4064/sm230729-14-12
Publication status	Published - 2024

Keywords

Muckenhoupt Ap weights
Riesz bounded variation spaces
Rubio de Francia extrapolation
Sobolev spaces
variable Lebesgue spaces

ASJC Scopus subject areas

General Mathematics

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10.4064/sm230729-14-12

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abstract = "We introduce weighted Riesz bounded variation spaces defined on an open subset of n-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia{\textquoteright}s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.",

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PY - 2024

Y1 - 2024

N2 - We introduce weighted Riesz bounded variation spaces defined on an open subset of n-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia’s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.

AB - We introduce weighted Riesz bounded variation spaces defined on an open subset of n-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia’s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.

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KW - Riesz bounded variation spaces

KW - Rubio de Francia extrapolation

KW - Sobolev spaces

KW - variable Lebesgue spaces

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A characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces

Abstract

Keywords

ASJC Scopus subject areas

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