%0 Journal Article
%T Pseudodifferential operators on -modulation spaces
%A Lasse Borup
%J Journal of Function Spaces and Applications
%D 2004
%I Hindawi Publishing Corporation
%R 10.1155/2004/621924
%X We study expansions of pseudodifferential operators from the Hörmander class in a special family of functions called brushlets. We prove that such operators have a sparse representation in a brushlet system. Using this sparsity, we show that a pseudodifferential operator extends to a bounded operator between α-modulation spaces. These spaces were introduced by Gröbner in [15]. They are, in some sense, intermediate spaces between the classical Besov and Modulation spaces.
%U http://www.hindawi.com/journals/jfsa/2004/621924/abs/