Revista de la
Unión Matemática Argentina
Affinity kernels on measure spaces and maximal operators
Hugo Aimar, Ivana Gómez, and Luis Nowak
Volume 63, no. 2 (2022), pp. 489–503

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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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