Weighted singular integral operators and non-homogenous harmonic analysis

October 10 to October 14, 2011

at the

American Institute of Mathematics, San Jose, 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
by  Steve Hofmann, Jose Maria Martell, and Svitlana Mayboroda,  Int. Math. Res. Not. IMRN 2014, no. 10, 2702-2729  MR3214282
Logarithmic bump conditions and the two weight boundedness of Calderon-Zygmund operators
by  David Cruz-Uribe, Alexander Reznikov, and Alexander Volberg,  Adv. Math. 255 (2014), 706-729  MR3167497
One and two weight norm inequalities for Riesz potentials
by  David Cruz-Uribe and Kabe Moen
Regularity of solutions to degenerate p-Laplacian equations
by  David Cruz-Uribe, Kabe Moen, and Virginia Naibo,  J. Math. Anal. Appl. 401 (2013), no. 1, 458-478  MR3011287
Pointwise convergence of Walsh--Fourier series of vector-valued functions
by  Tuomas P. Hytónen and Michael T. Lacey
Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
by  Tuomas P. Hytónen, Michael T. Lacey, and Carlos Pérez
Two weight inequality for the Hilbert transform: a real variable characterization
by  Michael T. Lacey, Eric T. Sawyer, Chun-Yen Shen, and Ignacio Uriarte-Tuero