Smooth Molecular Decompositions of Functions and Singular Integral Operators.; (Memoirs of the American Mathematical Society Number 742.)

Gilbert, J.E. et al.

ISBN 10: 0821827723 / ISBN 13: 9780821827727

Editore: American Mathematical Society, Providence, RI, 2000

74pp. As new, clean, tight & bright condition. Codice articolo 161987

Riassunto:

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.

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Titolo: Smooth Molecular Decompositions of Functions...
Casa editrice: American Mathematical Society, Providence, RI
Data di pubblicazione: 2000
Legatura: Paperback