Dear All,
on behalf of the organizers of the probability and analysis seminar (Vasileios and me), I would like to invite everybody to the seminar today. The details are below.
Oleksii.
We revisit basic nonhomogeneous Calderon-Zygmund theory from the point of view of martingales. Given a measure of polynomial growth on , we refine a deep result by David and Mattila to construct an atomic martingale filtration of which provides the right framework for a dyadic form of nondoubling harmonic analysis. Our dyadic formulation is effective to address some basic questions:
(i) A dyadic form of the `right' BMO space for non doubling measures, RBMO.
(ii) Lerner's domination of Calderon-Zygmund operators by dyadic operators.
(iii) A dyadic Calderon-Zygmund decomposition suitable for the study of both Calderon-Zygmund operators and Haar shifts.
If there is enough time, we will explain how the formulation of our results in terms of martingales leads to a natural generalization to matrix valued functions.
Based on joint work with Javier Parcet.