TY - BOOK ID - 136405904 TI - Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory AU - Hytönen, Tuomas. AU - van Neerven, Jan. AU - Veraar, Mark. AU - Weis, Lutz. PY - 2016 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Fourier analysis. KW - Measure theory. KW - Partial differential equations. KW - Probabilities. KW - Functional analysis. KW - Fourier Analysis. KW - Measure and Integration. KW - Partial Differential Equations. KW - Probability Theory and Stochastic Processes. KW - Functional Analysis. UR - https://www.unicat.be/uniCat?func=search&query=sysid:136405904 AB - 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 -