Harmonic and Geometric Analysis

  • Giovanna Citti
  • Loukas Grafakos
  • Carlos Pérez
  • Alessandro Sarti
  • Xiao Zhong

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Giovanna Citti, Alessandro Sarti
    Pages 1-55
  3. Carlos Pérez
    Pages 91-143
  4. Xiao Zhong
    Pages 145-170

About this book


This book presents an expanded version of four series of lectures delivered by the authors at the CRM.

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, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. 

The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differential equations in divergence form.


Heisenberg group maximal function multilinear Calderón-Zygmund operator weights

Authors and affiliations

  • Giovanna Citti
    • 1
  • Loukas Grafakos
    • 2
  • Carlos Pérez
    • 3
  • Alessandro Sarti
    • 4
  • Xiao Zhong
    • 5
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of MissouriColumbiaUSA
  3. 3.Departamento de Análisis MatemáticoUniversidad de SevillaSevillaSpain
  4. 4.Dipartimento di Elettronica, Informatica e SistemisticaUniversità di BolognaBolognaItaly
  5. 5.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

Bibliographic information