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Analysis Seminar – Jose Conde, Instituto de Ciencias Matematicas, Madrid, Spain
October 14, 2016 @ 10:00 am - 11:00 am
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:
- A dyadic form of the ‘right’ BMO space for non doubling measures, RBMO.
- Lerner’s domination of Caldero´n-Zygmund operators by dyadic opera- tors.
- 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.
- 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.