Analysis in Banach Spaces Volume I: Martingales and Littlewood-Paley Theory /

• Main Authors: Hytönen, Tuomas (Author), van Neerven, Jan (Author), Veraar, Mark (Author), Weis, Lutz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 63
• Subjects: Mathematics.; Fourier analysis.; Functional analysis.; Measure theory.; Partial differential equations.; Probabilities.; Fourier Analysis.; Measure and Integration.; Partial Differential Equations.; Probability Theory and Stochastic Processes.; Functional Analysis.

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 evolut...

Table of 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.