Monatshefte für Mathematik

, Volume 169, Issue 1, pp 15–32 | Cite as

Shearlet coorbit spaces: traces and embeddings in higher dimensions

  • Stephan Dahlke
  • Sören Häuser
  • Gabriele Steidl
  • Gerd Teschke
Article

Abstract

This papers examines structural properties of the recently developed shearlet coorbit spaces in higher dimensions. We prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone in three dimensions into Besov spaces. The results are based on general atomic decompositions of Besov spaces. Furthermore, we establish trace results for these subspaces with respect to the coordinate planes. It turns out that in many cases these traces are contained in lower dimensional shearlet coorbit spaces.

Keywords

Coorbit space theory Square-integrable group representations Banach frames Embedding of function spaces Besov spaces Trace theorems 

Mathematics Subject Classification

22D10 42C15 46E35 47B25 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Stephan Dahlke
    • 1
  • Sören Häuser
    • 2
  • Gabriele Steidl
    • 2
  • Gerd Teschke
    • 3
  1. 1.FB12 Mathematik und InformatikPhilipps-Universität MarburgMarburgGermany
  2. 2.Fachbereich für MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  3. 3.Institute for Computational Mathematics in Science and TechnologyHochschule Neubrandenburg, University of Applied SciencesNeubrandenburgGermany

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