On the composition operator with variable integrability

Carlos F. Álvarez; Javier Henríquez-Amador; John Millán G.; Eiver Rodríguez; Carlos F. Álvarez; Javier Henríquez-Amador; John Millán G.; Eiver Rodríguez

doi:10.3934/math.2025095

AIMS Mathematics

2025, Volume 10, Issue 2: 2021-2041. doi: 10.3934/math.2025095

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On the composition operator with variable integrability

1.
Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile
2.
Departamento de Matemáticas, Universidad del Valle, Ciudadela Universitaria Meléndez Edificio E20, Cali, Colombia
3.
Área de Básicas Exactas, Universidad del Sinú, Seccional Cartagena, Av. El Bosque, Transv. 54 Nº 30-729, Cartagena, Colombia
4.
Departamento de Matematicas, Universidad de Puerto Rico, 17 AVE Universidad STE 1701, San Juan, PR, USA

Received: 30 October 2024 Revised: 20 January 2025 Accepted: 22 January 2025 Published: 08 February 2025
MSC : 47B33, 46BE30

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.
- composition operators,
- variable exponent spaces,
- metric measure spaces,
- continuity,
- compactness
Citation: Carlos F. Álvarez, Javier Henríquez-Amador, John Millán G., Eiver Rodríguez. On the composition operator with variable integrability[J]. AIMS Mathematics, 2025, 10(2): 2021-2041. doi: 10.3934/math.2025095

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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.

References

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