Synopses & Reviews
Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón-Zygmund theory, for instance the Lp inequalities for Calderón-Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.
Synopsis
This volume contains two surveys of new results on linear and multilinear analysis. It offers an insightful presentation of the De Giorgi-Moser-Nash result and contains elegant applications of harmonic analysis to human vision.
Synopsis
This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.
Table of Contents
1 Models of the Visual Cortex in Lie Groups.- 2 Multilinear Calderón-Zygmund Singular Integrals.- 3 Singular Integrals and Weights.- 4 De Giorgi-Nash-Moser Theory.