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

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

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 74 p.
  • 言語 ENG
  • 商品コード 9780821827727
  • DDC分類 515.723

Full 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.