Affiliation:
1. 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.
Funder
R&D&I project
Programa de Ayudas de Investigación y Desarrollo
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference25 articles.
1. Krivine, J.L. (1973). Théorèmes de Factorisation dans les Espaces Réticulés, Séminaire Maurey-Schwartz.
2. Lindenstrauss, J., and Tzafriri, L. (1979). Classical Banach Spaces II: Function Spaces, Springer.
3. Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces;Defant;Positivity,2001
4. Diestel, J., Jarchow, H., and Tonge, A. (1995). Absolutely Summing Operators, Cambridge University Press.
5. Lp-approximation using fractal functions on the Sierpiński gasket;Agrawal;Results Math.,2022