Composition operators on Sobolev spaces and weighted moduli inequalities

Vladimir Gol'dshtein, Evgeny Sevost'yanov, Alexander Ukhlov

Research output: Working paper/PreprintPreprint

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Abstract

In this paper we study connections between composition operators on Sobolev spaces and mappings defined by $p$-moduli inequalities ($p$-capacity inequalities). We prove that weighted moduli inequalities lead to composition operators on corresponding Sobolev spaces and inverse, composition operators on Sobolev spaces imply weighted moduli inequalities.
Original languageEnglish
StatePublished - 21 Dec 2021

Keywords

  • math.AP
  • 46E35, 30C65

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