Workshop in Harmonic Analysis and its interaction with Operator Theory



At the intersection of the Summer School in Harmonic Analysis, Metric Spaces and Applications to P.D.E. and the 22nd International Workshop on Operator Theory and its Applications (IWOTA 2011) , there will be a workshop in harmonic analysis in Sevilla from 4 July to 8 July 2011 .

This workshop includes activities related to the Summer School, in particular Alexander Volberg's course entitled ``Ubiquitous Bellman functions, which contrary to common beliefs, continue to give new results, not old results'', as well as two thematic sessions of IWOTA 2011, entitled ``Harmonic Analysis, Inequalities and Homogenization Theory and Applications'' and ''Harmonic analysis of differential operators'' respectively. The sessions are described below.

Registration: the participants will need to register for IWOTA. Instructions are here.



Harmonic analysis of differential operators

Organisers: Pierre Portal and Andrea Carbonaro

Speakers:

  • Pascal Auscher (Orsay, France): Operators and maximal regularity on tent spaces.
  • Nadine Badr (Lyon, France): An atomic decomposition and maximal characterization of the Hajlasz Sobolev space M^1_1 on manifolds.
  • Frederic Bernicot (Lille, France): Multilinear multipliers and scattering problem.
  • Jorge Betancor (La Laguna, Spain): Variation operators for semigroups and Riesz transforms in $L^p$ and BMO spaces in the Schrodinger setting.
  • The Anh Bui (Macquarie, Australia): Sharp weighted Lp estimates for spectral multipliers without Gaussian estimates
  • Jacek Dziubanski (Wroclaw, Poland): Hardy spaces for Schrodinger operators.
  • Tuomas Hytonen (Helsinki, Finland): On the duality of nontangential maximal functions and Carleson measures.
  • Giancarlo Mauceri (Genova, Italy): Some new Hardy spaces on manifolds of negative curvature and higher order Riesz transforms.
  • Svitlana Mayboroda (Purdue, USA): Elliptic boundary problems with rough coefficients.
  • Andrew Morris (Columbia-Missouri, USA): An Embedding for Hardy Spaces on Riemannian Manifolds.
  • Jan van Neerven (Delft, The Netherlands): Stochastic maximal regularity.
  • Emmanuel Russ (Marseille, France): Some results about the inversion of the divergence operator.
  • Peter Sjogren (Chalmers, Sweden): Calderon-Zygmund operators related to Jacobi expansions.
  • Pablo Stinga (Madrid, Spain): Fractional operators with semigroups in PDEs and Harmonic Analysis.
  • Maria C. Reguera (Georgia Tech, USA): The Maximal Function and Hilbert Transform on Weighted Spaces: Theorems and Examples.
  • Alexander Reznikov (Michigan State, USA): Solution of $A_1$ conjecture via Bellman function technique.

Harmonic Analysis, Inequalities and Homogenization Theory and Applications

Organisers: Lars-Erik Persson and Natasha Samko

Speakers:

  • Shoshana Abramovich (Israel): Subadditivity, Generalized Jensen Inequalities and Superquadracity.
  • Alexandre Almeida (Portugal): Sublinear operators on Herz spaces with variable exponents.
  • Ahmad Al-Salman (Jordan): A Class of Marcinkiewicz Integrals Related to Bochner-Riesz operators.
  • Gregory Chechkin (Russia): Thick Junctions with Concentrated Masses.
  • Peter Hasto (Finland): Muckenhoupt weights in variable exponent spaces.
  • Anders Holmbom (Sweden): On some generalization and variants of two-scale convergence and their application.
  • Vakhtang Kokilashvili (Georgia): The Fourier operators in weighted grand Lebesgue spaces.
  • Katsuo Matsuoka (Japan): Singular and fractional integral operators on new function spaces.
  • Carlos Perez (Spain): Quadratic and subexponential decay estimates for commutators of singular integral operators.
  • Lars-Erik Persson (Sweden): Quasi-monotone weight functions and their characteristics and applications.
  • Humberto Rafeiro (Portugal): Variable exponent Campanato spaces.
  • Maria Alessandra Ragusa (Italy): On classical operators of real analysis having vanishing mean oscillation functions.
  • Ezequiel Rela (Spain): Furstenberg sets and Hausdorff measures.
  • S. Saitoh (Japan): Applications of the theory of reproducing kernels to convolutions and integral transforms
  • Natasha Samko (Portugal): Weighted estimates of the Cauchy singular integral operator in generalized Morrey spaces.
  • Stefan Samko (Portugal): On potentials in generalized Holder spaces over uniform domains.
  • Aida Sahmurova (Turkey): Singular Perturbation problems occurring in atmospheric dispersion of pollutants.
  • Veli Shakhmurov (Turkey): Separable differential operators in Banach spaces and applications.
  • Salaudin Umarkhadzhiev (Russia): Hardy operators in grand Lebesgue spaces.

Description: Many fundamental objects of harmonic analysis can be thought of as being associated with standard differential operators. Fourier multipliers and Littlewood-Paley decompositions, for example, are closely related to the functional calculus of the laplacian. This point of view has led to recent developments in harmonic analysis that exploit the operator theory of relevant differential operators to adapt classical results to new contexts.
A typical example is given by Hardy space theory on Riemannian manifolds, which is based on the functional calculus of the Hodge-de Rham laplacian. There is, however, great diversity in this field, with somewhat disconnected teams studying elliptic operators with rough coefficients, Schrodinger operators, geometric laplacians, Ornstein-Uhlenbeck operators...
The goal of this thematic session is to bring together some of the researchers involved to share ideas, recognising the common thread in these recent developments. 		Description: Harmonic Analysis, Inequalities and Homogenization Theory and Applications are increasingly important areas for various kinds of applications both to other fields of Mathematics and to other sciences, e.g. physics, material science, numerical analysis and geophysics. The main aim of the session is to bring together researchers with different backgrounds and interests in all aspects of these areas of mathematics and plan for future cooperation and new directions of joint research. As background the participants will present the newest developments and present ``state of art'' of their research fields. The topics of interest include (but are not limited to): Harmonic Analysis, General and Hardy type Inequalities, Real Analysis, Interpolation Theory, Function Spaces, Homogenization Theory. Summing up, we invite all interested researchers in the areas described above to participate.