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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Roger Arnau & Enrique A. Sánchez-Pérez, 2023. "Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4599-:d:1277339
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