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Journal of Function Spaces and Applications
Volume 2012, Article ID 163213, 47 pages
http://dx.doi.org/10.1155/2012/163213
Research Article

Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits

Hausdorff Center for Mathematics, Institute for Numerical Simulation, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Received 7 April 2010; Accepted 20 July 2010

Academic Editor: Hans Triebel

Copyright © 2012 Tino Ullrich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces (H. Triebel 1983, 1992, and 2006) in terms of continuous local means for the full range of parameters. In particular, we prove characterizations in terms of Lusin functions (tent spaces) and spaces involving the Peetre maximal function to apply the classical coorbit space theory according to Feichtinger and Gröchenig (H. G Feichtinger and K. Gröchenig 1988, 1989, and 1991). This results in atomic decompositions and wavelet bases for homogeneous spaces. In particular we give sufficient conditions for suitable wavelets in terms of moment, decay and smoothness conditions.