Harmonic Analysis

Scope of the special session

This special session is focused on harmonic analysis and its numerous interactions with other areas of research in analysis and more generally in mathematics. 

The field of harmonic analysis has grown significantly in recent years and has embraced a large number of topics in connection with other areas of mathematics. We briefly mention applications to nonlinear differential equations, in particular dispersive equations but not only, geometric analysis, complex analysis in one and several variables, analysis on manifolds, ergodic theory, analytic number theory, combinatorics; and others.

Within the classical harmonic analysis many topics received great attention. We mention singular integrals defined by the newly considered problems and hence presenting a variety of types of singularities, singular integrals and the theory of weights, operators defined by oscilllatory integrals, geometric measure theory, multilinear operators, and several others.

The spirit of this special session perfectly fits in the framework of the conference, whose main goal is to share recent developements by researchers of many different areas in mathematics, because of the wide range of topics related to harmonic analysis which are covered by this session.

Organisers

  • Albert Mas (Autonomous University of Barcelona, Spain) - amasblesa@gmail.com
  • Marco Peloso (University of Milan, Italy)

Abstracts and schedule

Below you can download the schedule and the abstracts of all talks of this special session.

Speakers

  • Vasilis Chousionis (University of Helsinki, Finland)

           Square functions and uniform rectifiability

  • Leonardo Colzani (University of Milan, Italy)

           Localization and convergence of Fourier series and integrals

  • Javier Duoandikoetxea (University of the Basque Country, Spain)

           A comparison of the characterizations of A

  • Bruno Franchi (University of Bologna, Italy)

           Differential forms in Heisenberg groups and div-curl systems

  • Gustavo Garrigós (University of Murcia, Spain)

           Maximal functions, weights and convergence to initial data of certain Poisson equations

  • José María Martell (ICMAT, Autonomous University of Madrid, Spain)

          The Dirichlet problem for elliptic systems in the upper-half space

  • Alessio Martini (Christian-Albrechts University of Kiel, Germany)

           Hypoelliptic operators and sharp multiplier theorems

  • Joan Mateu (Autonomous University of Barcelona, Spain)

           Euler equation and vortex patches

  • Carlos Pérez (University of Sevilla, Spain)

           Around a conjecture of E. Sawyer for the Hilbert transform and weights

  • Ezequiel Rela (University of Sevilla, Spain)

          Optimality of weighted estimates without examples

  • Fulvio Ricci (Scuola Normale Superiore di Pisa, Italy)

           Hardy and uncertainty inequalities on stratified groups

  • Ignacio Uriarte-Tuero (Michigan State University, USA)

           Two weight norm inequalities for singular and fractional integral operators in Rn

  • Maria Vallarino (Polytechnic University of Turin, Italy)

           Schrödinger equations on Damek-Ricci spaces