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2021 Extension of Lipschitz-type operators on Banach function spaces
Wasthenny V. Cavalcante, Pilar Rueda, Enrique A. Sánchez-Pérez
Topol. Methods Nonlinear Anal. 57(1): 343-364 (2021). DOI: 10.12775/TMNA.2020.026

Abstract

We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced. We analyze Lipschitz-type inequalities in two fundamental cases. The first concerns almost everywhere pointwise inequalities, while the second considers dominations involving integrals. These Lipschitz-type inequalities provide a suitable frame to work with operators that take values on Banach function spaces. In the last part of the paper we use some interpolation procedures to extend our study to interpolated Banach function spaces.

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Wasthenny V. Cavalcante. Pilar Rueda. Enrique A. Sánchez-Pérez. "Extension of Lipschitz-type operators on Banach function spaces." Topol. Methods Nonlinear Anal. 57 (1) 343 - 364, 2021. https://doi.org/10.12775/TMNA.2020.026

Information

Published: 2021
First available in Project Euclid: 5 March 2021

Digital Object Identifier: 10.12775/TMNA.2020.026

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 1 • 2021
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