Weighted Hardy spaces / Jan-Olov Strömberg, Alberto Torchinsky

Two of the most active areas of investigation in harmonic analysis over the past two decades involve Hardy spaces and the theory of weights. This book is concerned with weighted Hardy spaces, presenting a comprehensive introduction to both. The heart of the book contains four chapters on weighted Hardy spaces, including sections on atomic decompositions and duality.
The first two chapters introduce weights, in enough generality to include homogeneous spaces. Doubling, reverse Hölder, and Ap conditions are discussed, along with the Jones decomposition of weights. The next three chapters contain the background information needed to define the Hardy spaces. The book ends with a discussion of singular integral and multiplier operators and interpolation of these spaces. Researchers in the field will find this monograph useful, since it contains much of the current theory. (MathSciNet)