Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces / Y. S. Han, E. T. Sawyer.

Format:

Book

Author/Creator:

Han, Yongsheng, author.

Sawyer, E. T. (Eric T.), 1951- author.

Series:

Memoirs of the American Mathematical Society ; Number 530.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 530

Language:

English

Subjects (All):

Littlewood-Paley theory.

Multipliers (Mathematical analysis).

Hardy spaces.

Function spaces.

Physical Description:

1 online resource (138 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Language Note:

English

Summary:

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calderón reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Contents:

""Contents""; ""Â1. Introduction""; ""Â2. T[sup(â€?1)][sub(N)] is a Calderónâ€?Zygmund operator""; ""Â3. The Calderónâ€?type reproducing formula on spaces of homogeneous type""; ""Â4. The Besov and Triebelâ€?Lizorkin spaces on spaces of homogeneous type""; ""Â5. The T1 theorems for B[sup(α,q)][sub(p)] and F[sup(α,q)][sub(p)]""; ""Â6. Atomic decomposition of B[sup(α,q)][sub(p)] and F[sup(α,q)][sub(p)]""; ""Â7. Duality and interpolation of B[sup(α,q)][sub(p)] and F[sup(α,q)][sub(p)]""; ""References""

Notes:

"July 1994, Volume 110, Number 530 (fifth of 6 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0109-6