Abstract
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.
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.
| Original language | English |
|---|---|
| Place of Publication | Cham |
| Publisher | Springer |
| Number of pages | 492 |
| ISBN (Electronic) | 978-3-319-48520-1 |
| ISBN (Print) | 978-3-319-48519-5 |
| DOIs | |
| Publication status | Published - 2016 |
Publication series
| Name | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge |
|---|---|
| Publisher | Springer International Publishing |
| Volume | 63 |
| ISSN (Print) | 0071-1136 |
Keywords
- Fourier Analysis
- Measure and Integration
- Partial Differential Equations
- Peobability Theory and Stochastic Processes
- Functional Analysis