Smooth molecular decompositions of functions and singular integral operators
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Bibliographic Information
Smooth molecular decompositions of functions and singular integral operators
（Memoirs of the American Mathematical Society, no. 742）
American Mathematical Society, 2002
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Note
"March 2002, volume 156, number 742 (third of 5 numbers)"
Includes bibliography (p. 73-74)
Description and Table of Contents
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.
Table of Contents
Main results Molecular decompositions of operators Frames Maximal theorems and equi-convergence Appendix. Proof of basic estimates.
by "Nielsen BookData"
