Analysis in Banach spacesnVolume 1, Martingales and Littlewood-Paley theory

Description

The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes.  The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas. Front Matter....Pages i-xvii Bochner spaces....Pages 1-66 Operators on Bochner spaces....Pages 67-164 Martingales....Pages 165-266 UMD spaces....Pages 267-372 Hilbert transform and Littlewood–Paley theory....Pages 373-492 Back Matter....Pages 493-614