Memoirs of the American Mathematical Society 1994; 126 pp; softcover Volume: 110 ISBN10: 0821825925 ISBN13: 9780821825921 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/110/530
 In this work, Han and Sawyer extend LittlewoodPaley theory, Besov spaces, and TriebelLizorkin 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 bmoment, and LittlewoodPaley characterizations of Besov and TriebelLizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity. Readership Research mathematicians. Table of Contents  Introduction
 \(T_N^{1}\) is a CalderónZygmund operator
 The Calderóntype reproducing formula on spaces of homogeneous type
 The Besov and TriebelLizorkin 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
