Smooth Molecular Decompositions of Functions and Singular Integral Operators

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

ISBN 10: 0821827723 / ISBN 13: 9780821827727

Published by Amer Mathematical Society, 2002

Former library book; Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0821827723I3N10

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.

Bibliographic Details

Title: Smooth Molecular Decompositions of Functions...
Publisher: Amer Mathematical Society
Publication Date: 2002
Binding: Unknown
Condition: Good
Dust Jacket Condition: No Jacket