Analysis in Banach Spaces: Volume I: Martingales and Littlewood-Paley Theory

By Jan van Neerven, Tuomas Hytönen, Mark Veraar

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.

• Format: Paperback
• Language: English
• ISBN: 3319839616
• ISBN13: 9783319839615
• Release Date: July 2018
• Publisher: Springer
• Length: 614 Pages
• Weight: 1.93 lbs.
• Dimensions: 1.3" x 6.1" x 9.2"