Composition operators in generalized Morrey spaces
Alexey Karapetyants
Southern Federal University, Rostov-on-Don, RussiaMassimo Lanza de Cristoforis
Università degli Studi di Padova, Italy
Abstract
Let be an open subset of . Let be a Borel measurable function from to . We prove necessary and sufficient conditions on in order that the composite function belongs to a generalized Morrey space whenever belongs to . Then we prove necessary conditions and sufficient conditions on in order that the composition operator be continuous, uniformly continuous, Hölder continuous and Lipschitz continuous in . We also consider its ‘vanishing’ generalized Morrey subspace and prove the related results for the composition operator as operator acting from to and also between the spaces . For the uniform, Hölder and Lipschitz continuity, we also have conditions that are both necessary and sufficient. We also have both necessary and sufficient conditions for the continuity under certain additional natural assumptions. We also consider the most commonly used Morrey classes that are related to power-type weights in the context of a discussion of some of the conditions that we impose on the weights.
Cite this article
Alexey Karapetyants, Massimo Lanza de Cristoforis, Composition operators in generalized Morrey spaces. Z. Anal. Anwend. 41 (2022), no. 3/4, pp. 259–299
DOI 10.4171/ZAA/1715