Analysis in Banach Spaces: Volume I: Martingales and Littlewood-Paley Theory: 1
Analysis in Banach Spaces: Volume I: Martingales and Littlewood-Paley Theory: 1 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Tuomas Hytönen
English | 16 Dec. 2016 | ISBN: 3319485199 | 634 Pages | PDF | 6.34 MB
English | 16 Dec. 2016 | ISBN: 3319485199 | 634 Pages | PDF | 6.34 MB
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.