Weighted singular integral operators and non-homogenous harmonic analysis

October 10 to October 14, 2011

at the

American Institute of Mathematics, Palo Alto, California

organized by

Svitlana Mayboroda, Maria Carmen Reguera, and Alexander Volberg

Original Announcement

This workshop will focus on recent developments on weighted inequalities for singular integral operators and its connection with questions in geometric measure theory and PDE. There are two central problems: In this workshop we aim to overview the competing methods that have been used to study the main problems: the martingale method adapted from the one-weight case, the maximum principle technique, and the Bellman function technique. As well as identify interesting directions for further work in areas that include operator theory, orthogonal polynomials, elliptic pdes, and weighted inequalities of all types in novel settings. The workshop will serve as a time and place to enhance the collaboration of several different groups working at this array of questions.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:
Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains
Logarithmic bump conditions and the two weight boundedness of Calderon-Zygmund operators
One and two weight norm inequalities for Riesz potentials
Regularity of solutions to degenerate p-Laplacian equations
Pointwise convergence of Walsh--Fourier series of vector-valued functions
Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
Two weight inequality for the Hilbert transform: a real variable characterization