Sobolev lifting over invariants

Armin Rainer, Adam Parusinski

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We prove lifting theorems for complex representations V of finite groups G. Let s = (s 1, …, s n) be a minimal system of homogeneous basic invariants and let d be their maximal degree. We prove that any continuous map f: R m ? V such that f = s ? f is of class C d-1,1 is locally of Sobolev class W 1,p for all [formula presented]In the case m = 1 there always exists a continuous choice f for given [formula presented]We give uniform bounds for the W 1,p-norm of f in terms of the C d-1,1-norm of f. The result is optimal: in general a lifting f cannot have a higher Sobolev regularity and it even might not have bounded variation if f is in a larger Hölder class.

OriginalspracheEnglisch
Aufsatznummer037
Seitenumfang31
FachzeitschriftSymmetry, Integrability and Geometry: Methods and Applications
Jahrgang17
DOIs
PublikationsstatusVeröffentlicht - 2021

ÖFOS 2012

  • 101002 Analysis
  • 101009 Geometrie

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