Smooth molecular decompositions of functions and singular integral operators / J.E. Gilbert [and five others].

Format:

Book

Author/Creator:

Gilbert, John E., author.

Contributor:

Gilbert, John E.

Series:

Memoirs of the American Mathematical Society ; no. 742.

Memoirs of the American Mathematical Society, 0065-9266 ; number 742

Language:

English

Subjects (All):

Function spaces.

Integral operators.

Decomposition (Mathematics).

Physical Description:

1 online resource (89 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ 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 ter

Contents:

""Contents""; ""Chapter 1. Main results""; ""1 Frame decompositions""; ""2 Molecular boundedness and operator decompositions""; ""3 Molecules and the affine group""; ""Chapter 2. Molecular decompositions of operators""; ""1 Smooth Calderón�Zygmund operators""; ""2 Cotlar type operators""; ""3 Kernel estimates""; ""4 Boundedness on spaces of molecules""; ""5 Triebel�Lizorkin spaces""; ""Chapter 3. Frames""; ""1 Continuity of group action""; ""2 Inversion of frame operator""; ""3 Convergence in Triebel�Lizorkin spaces""; ""4 Algebras of singular integral operators""

""Chapter 4. Maximal theorems and equ�convergence""""1 Introduction""; ""2 Equiconvergence""; ""3 Almost everywhere convergence of wavelet frame expansions""; ""4 Affine approximations to the identity""; ""Appendix. Proof of Basic Estimates""

Notes:

"Volume 156, number 742 (third of 5 numbers)."

Includes bibliographical references (pages 73-74).

Description based on print version record.

ISBN:

1-4704-0335-8