Hytönen T., van Neerven J., Veraar M., Weis L. Analysis in Banach Spaces. Volume I: Martingales and Littlewood-Paley Theory

Springer International Publishing AG, 2016. — 628 p. — (A Series of Modern Surveys in Mathematics 63) — ISBN: 3319485199The 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.Bochner spaces
Operators on Bochner spaces
Martingales
UMD spaces
Hilbert transform and Littlewood–Paley theory
Appendices
Open problems
Measure theory
Banach spaces
Interpolation theory
Schatten classes