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Journal of Function Spaces and Applications
Volume 8, Issue 2, Pages 129-165
http://dx.doi.org/10.1155/2010/469513

Atomic, molecular and wavelet decomposition of generalized 2-microlocal Besov spaces

Mathematical Institute, Friedrich Schiller University, Ernst-Abbe-Platz 2, 07737 Jena, Germany

Received 1 July 2008

Academic Editor: Hans Triebel

Copyright © 2010 Hindawi Publishing Corporation. 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 introduce generalized 2-microlocal Besov spaces and give characterizations in decomposition spaces by atoms, molecules and wavelets. We apply the wavelet decomposition to prove that the 2-microlocal spaces are invariant under the action of pseudodifferential operators of order 0.