Memoirs of the American Mathematical Society 2002; 74 pp; softcover Volume: 156 ISBN10: 0821827723 ISBN13: 9780821827727 List Price: US$53 Individual Members: US$31.80 Institutional Members: US$42.40 Order Code: MEMO/156/742
 Under minimal assumptions on a function \(\psi\) we obtain wavelettype frames of the form \[\psi_{j,k}(x) = r^{(1/2)n j} \psi(r^j x  sk), \qquad j \in \mathbb{Z}, k \in \mathbb{Z}^n,\] for some \(r > 1\) and \(s > 0\). This collection is shown to be a frame for a scale of TriebelLizorkin 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. Readership Graduate students and research mathematicians interested in functional analysis, CalderónZygmund theory, singular integral operators, and wavelets. Table of Contents  Main results
 Molecular decompositions of operators
 Frames
 Maximal theorems and equiconvergence
 Appendix. Proof of basic estimates
