Affinity kernels on measure spaces and maximal operators

Authors

  • Hugo Aimar Instituto de Matemática Aplicada del Litoral, UNL, CONICET; CCT CONICET Santa Fe, Predio “Alberto Cassano”, Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
  • Ivana Gómez Instituto de Matemática Aplicada del Litoral, UNL, CONICET; CCT CONICET Santa Fe, Predio “Alberto Cassano”, Colectora Ruta Nac. 168 km 0, Paraje El Pozo, S3007ABA Santa Fe, Argentina
  • Luis Nowak Instituto de Investigación en Tecnologías y Ciencias de la Ingeniería, CONICET, UNComa; Departamento de Matemática, FaEA, Neuquén, Argentina

DOI:

https://doi.org/10.33044/revuma.2518

Abstract

In this note we consider maximal operators defined in terms of families of kernels and families of their level sets. We prove a general  estimate that extends some classical Euclidean cases and, under some mild transitivity property, we show their basic boundedness  properties on Lebesgue spaces. The motivation of these problems has its roots in the analysis associated to affinity kernels on large  data sets.

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References

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Published

2022-12-20

Issue

Vol. 63 No. 2 (2022)

Section

Article

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Copyright (c) 2022 Hugo Aimar, Ivana Gómez, Luis Nowak

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