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Analysis in Banach Spaces

Volume I: Martingales and Littlewood-Paley Theory

Lutz Weis, Mark Veraar, Jan van Neerven, et al.

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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

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.

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Schlagwörter

UMD Spaces, 46Bxx, 42Bxx, 60Gxx, Fourier multipliers, Bochner integration, Hilbert transform, partial differential equations, Conditional Expectations