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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.
| Autorius: | Tuomas Hytönen, Lutz Weis, Mark Veraar, Jan Van Neerven, |
| Serija: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2016 |
| Knygos puslapių skaičius: | 632 |
| ISBN-10: | 3319485199 |
| ISBN-13: | 9783319485195 |
| Formatas: | 241 x 160 x 40 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Analysis in Banach Spaces: Volume I: Martingales and Littlewood-Paley Theory“
