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Analysis in Banach Spaces - Volume I: Martingales and Littlewood-Paley Theory (Paperback, Softcover reprint of the original 1st ed. 2016)
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Analysis in Banach Spaces - Volume I: Martingales and Littlewood-Paley Theory (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 63
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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.
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