Conde-Alonso, Jos´e Manuel (Universitat Aut`onoma de Barcelona, Spain):  A dyadic RBMO space and pointwise domination of nonhomogeneous Calder´on- Zygmund operators.

Abstract: We revisit basic nonhomogeneous Caldero´n-Zygmund theory from the point of view of martingales. Given a measure µ of polynomial growth on Rd, we refine a deep result by David and Mattila to construct an atomic martingale filtration of supp(µ) which provides the right framework for a dyadic form of nondoubling harmonic analysis. Our dyadic formulation is effective to address some basic questions:

1. A dyadic form of the ‘right’ BMO space for non doubling measures, RBMO.
2. Lerner’s domination of Caldero´n-Zygmund operators by dyadic opera- tors.
3. A dyadic Caldero´n-Zygmund decomposition suitable for the study of both Caldero´n-Zygmund operators and Haar shifts.Based on joint work with Javier Parcet.
4. 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.