Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces

Roger Arnau and Enrique A. Sánchez-Pérez ()
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Roger Arnau: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
Enrique A. Sánchez-Pérez: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain

Mathematics, 2023, vol. 11, issue 22, 1-13

Abstract: We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties ( p -convexity, p -concavity, p -regularity) or, equivalently, some types of summability conditions (for example, when the terms of the terms in the sums in the range of the operator are restricted to the interval [ − 1 , 1 ] ) can be studied by adapting the classical analytical techniques of the summability of operators on Banach lattices, which recalls the work of Maurey. We show a technique to prove new integral dominations (equivalently, operator factorizations), which involve non-homogeneous expressions constructed by pointwise composition with Lipschitz maps. As an example, we prove a new family of integral bounds for certain operators on Lorentz spaces.

Keywords: banach function space; lipschitz transform; integral inequality; p -convexity; p -concavity; p -regular operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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