TY  - BOOK
AU  - Hytonen,Tuomas
AU  - Neerven,Jan van
AU  - Veraar,Mark
AU  - Weis,Lutz
TI  - Analysis in Banach spaces
T2  - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics
SN  - 9783319485195
U1  - 515.732   23
PY  - 2016///
CY  - Cham
PB  - Springer
KW  - Banach spaces
N1  - Vol 1: Martingales and Littlewood-Paley theory; Includes bibliographical references and index; 1. Bochner spaces --
2. Operators on Bochner spaces --
3. Martingales --
4. MUD spaces --
5. Hilbert transform and Littlewood-Paley theory --
O Open problems --
A Measure theory --
B Banach spaces --
C Interpolation theory --
D Schatten classes
N2  - 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
ER  -