Description

• Title:
  Extension of Lipschitz-type operators on Banach function spaces
• Creator:
  Cavalcante, Wasthenny V.;
  Rueda, Pilar;
  Sánchez-Pérez, Enrique A.
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 343 - 364;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.026/28141 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.026/28142
• Subject:
  Lipschitz operator;
  Banach function space;
  integration;
  measure;
  metric space;
  Primary;
  26A16;
  46E30;
  Secondary;
  47H99
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.026
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other