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

By: Y.S. Han (author), D. Weiland (author), Joseph D. Lakey (author), J.E. Gilbert (author), J.A. Hogan (author)Paperback

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### Description

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.

### Contents

Main results Molecular decompositions of operators Frames Maximal theorems and equi-convergence Appendix. Proof of basic estimates.

### Product Details

• ISBN13: 9780821827727
• Format: Paperback
• Number Of Pages: 74
• ID: 9780821827727
• ISBN10: 0821827723

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