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)

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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