Smooth Molecular Decompositions of Functions and Singular Integral Operators (Memoirs of the American Mathematical Society) - Softcover

Gilbert, J.E.; Han, Y.S.; Hogan, J.A.; Lakey, Joseph D.; Weiland, D.

Softcover

ISBN 10: 0821827723 ISBN 13: 9780821827727

Publisher: American Mathematical Society, 2002

Synopsis

Under minimal assumptions on a function $\psi$ we obtain wavelet-type frames of the form $\psi_{j,k}(x) = r^{(1/2)n j} \psi(r^j x - sk), j \in \integer, k \in \integer^n,$ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in terms of smooth molecules.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2002
• Language: English
• ISBN 10: 0821827723
• ISBN 13: 9780821827727
• Binding: Mass Market Paperback
• Number of pages: 74