Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces
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Bibliographic Information
Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces
（Memoirs of the American Mathematical Society, no. 530）
American Mathematical Society, 1994
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Note
"July 1994, volume 110, number 530 (fifth of 6 numbers)" -- T.p
Includes bibliographical references (p. 125-126)
Description and Table of Contents
Description
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 Calderon 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.
Table of Contents
Introduction $T_N^{-1}$ is a Calderon-Zygmund operator The Calderon-type reproducing formula on spaces of homogeneous type The Besov and Triebel-Lizorkin spaces on spaces of homogeneous type The $T1$ theorems of $\dot B_p^{\alpha,q}$ and $\dot F_p^{\alpha,q}$ Atomic decomposition of $\dot B_p^{\alpha,q}$ and $\dot F_p^{\alpha,q}$ Duality and interpolation of $\dot B_p^{\alpha,q}$ and $\dot F_p^{\alpha,q}$ References.
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