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Research Article | Open Access

On the composition operator with variable integrability

Carlos F. Álvarez1( ), Javier Henríquez-Amador2, John Millán G.3, Eiver Rodríguez4
Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile
Departamento de Matemáticas, Universidad del Valle, Ciudadela Universitaria Meléndez Edificio E20, Cali, Colombia
Área de Básicas Exactas, Universidad del Sinú, Seccional Cartagena, Av. El Bosque, Transv. 54 Nº 30-729, Cartagena, Colombia
Departamento de Matematicas, Universidad de Puerto Rico, 17 AVE Universidad STE 1701, San Juan, PR, USA
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Abstract

In this article, we considered a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of the variable exponent, we provided necessary and sufficient conditions for this class of operators to be bounded and compact, respectively. In addition, we showed the usefulness of the variable change to study weak compactness properties in the framework of non-standard spaces.

Keywords

composition operatorsvariable exponent spacesmetric measure spacescontinuitycompactness
CLC number: 47B33, 46BE30

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2021-2041
DOI: 10.3934/math.2025095

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Cite this article:
Álvarez CF, Henríquez-Amador J, Millán G. J, et al. On the composition operator with variable integrability. AIMS Mathematics, 2025, 10(2): 2021-2041. https://doi.org/10.3934/math.2025095

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Received: 30 October 2024
Revised: 20 January 2025
Accepted: 22 January 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)