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Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis.
LIBRA 510.8 Er36 bd.1-5; n.s. hft.1-20,hft.22-29,hft.31-37
Available from offsite location
- Format:
- Book
- Author/Creator:
- Hytönen, Tuomas., Author.
- van Neerven, Jan., Author.
- Veraar, Mark., Author.
- Weis, Lutz., Author.
- Series:
- Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 ; 63
- Language:
- English
- Subjects (All):
- Fourier analysis.
- Measure theory.
- Differential equations, Partial.
- Probabilities.
- Functional analysis.
- Fourier Analysis.
- Measure and Integration.
- Partial Differential Equations.
- Probability Theory and Stochastic Processes.
- Functional Analysis.
- Local Subjects:
- Fourier Analysis.
- Measure and Integration.
- Partial Differential Equations.
- Probability Theory and Stochastic Processes.
- Functional Analysis.
- Physical Description:
- 1 online resource (XVII, 614 p. 3 illus.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Summary:
- 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.
- Contents:
- 1.Bochner Spaces
- 2.Operators on Bochner Spaces
- 3.Martingales
- 4.UMD spaces
- 5. Hilbert transform and Littlewood-Paley Theory
- 6.Open Problems
- A.Mesaure Theory
- B.Banach Spaces
- C.Interpolation Theory
- D.Schatten classes.
- Notes:
- Includes bibliographical references and index.
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