Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

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.Han, Y. S. is the author of 'Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces' with ISBN 9780821825921 and ISBN 0821825925.