num_pages: 126
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 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 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.
language: English
title: Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces
titlecomplete: Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces (Memoirs of the American Mathematical Society)
publisher: Amer Mathematical Society