Analysis in Banach Spaces
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…
Read More ↓Title Statements
- Full title :Analysis in Banach Spaces / Tuomas Hytönen, [et al.].
Summary
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.
Read More ↓Edition Statements
- Publication Date:cop. 2016.
Publication Statements
- Publisher(s):Springer, Springer International Publishing
- Language:und
- Publication Date:cop. 2016.
The Physical Object
- Description:XVII, 614 p.; : 24cm.
Edition Identifiers
- ISBN:9783319485195, 3319485199
- oclc:on1041609002
- LC Classification:QA322.2
Table of Contents
1.Bochner Spaces -- 2.Operators on Bochner Spaces -- 3.Martingales -- 4.UMD spaces -- 5. Hilbert transform and Littlewood-Paley Theory -- 6.Open Problems -- A.Mesaure Theory -- B.Banach Spaces -- C.Interpolation Theory -- D.Schatten classes.
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