Composition operators in generalized Morrey spaces

  • Alexey Karapetyants

    Southern Federal University, Rostov-on-Don, Russia
  • Massimo Lanza de Cristoforis

    Università degli Studi di Padova, Italy
Composition operators in generalized Morrey spaces cover

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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