Analysis in Banach Spaces
Volume I: Martingales and Littlewood-Paley Theory
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Beschreibung
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.
Presents a comprehensive and unified account of modern tools for the study of partial differential equations, harmonic analysis, and stochastic analysis in infinite dimensions Develops a systematic theory of UMD spaces, starting from scratch and reaching substantial Fourier-analytic applications Offers complete, detailed proofs with explicit bounds for most constants, many of them previously unrecorded in the literature Includes supplementary material: sn.pub/extras
Autor*in
Tuomas Hytönen
Themen in »Analysis in Banach Spaces«
46Bxx, 42Bxx, 60Gxx UMD Spaces Bochner integration Conditional Expectations Hilbert transform Fourier multipliers partial differential equations
Stimmen zu »Analysis in Banach Spaces«
“The book can be used not only as a reference book but also as a basis for advanced courses in vector-valued analysis and geometry of Banach spaces. This monograph can be studied for different motivations, it clearly goes straight to the core and introduces only those concepts that will be needed later on, but makes detailed proofs, so it can be used as a textbook for students or as a book for researchers … .” (Oscar Blasco, zbMATH, Vol. 1366.46001, 2017)
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