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Journal of Function Spaces and Applications
Volume 6 (2008), Issue 2, Pages 107-154

On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators

Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, Denmark

Received 1 May 2007

Academic Editor: Hans Feichtinger

Copyright © 2008 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.


A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space d is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on d and a suitable decomposition function. The decomposition function governs the structure of the decomposition of the frequency space, and for a very particular choice of decomposition function the spaces are reduced to classical (anisotropic) Triebel-Lizorkin spaces. An explicit atomic decomposition of the Triebel-Lizorkin type spaces is provided, and their interpolation properties are studied. As the main application, we consider Hörmander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.