Memoirs of the American Mathematical Society 2001; 80 pp; softcover Volume: 154 ISBN10: 0821827340 ISBN13: 9780821827345 List Price: US$52 Individual Members: US$31.20 Institutional Members: US$41.60 Order Code: MEMO/154/731
 We show that the class of weights \(w\) for which the Calderón operator is bounded on \(L^p(w)\) can be used to develop a theory of real interpolation which is more general and exhibits new features when compared to the usual variants of the LionsPeetre methods. In particular we obtain extrapolation theorems (in the sense of Rubio de Francia's theory) and reiteration theorems for these methods. We also consider interpolation methods associated with the classes of weights for which the Calderón operator is bounded on weighted Lorentz spaces and obtain similar results. We extend the commutator theorems associated with the real method of interpolation in several directions. We obtain weighted norm inequalities for higher order commutators as well as commutators of fractional order. One application of our results gives new weighted norm inequalities for higher order commutators of singular integrals with multiplications by BMO functions. We also introduce analogs of the space BMO in order to consider the relationship between commutators for Calderón type operators and their corresponding classes of weights. Readership Graduate students and research mathematicians interested in functional analysis. Table of Contents  Introduction
 Calderón weights
 Applications to real interpolation: reiteration and extrapolation
 Other classes of weights
 Extrapolation of weighted norm inequalities via extrapolation theory
 Applications to function spaces
 Commutators defined by the Kmethod
 Generalized commutators
 The quasi Banach case
 Applications to harmonic analysis
 BMO type spaces associated to Calderón weights
 Atomic decompositions and duality
 References
