Analysis Seminar: "A two weight inequality for Calderon-Zygmind operators on spaces of homogenous type with applications"
Speaker: Manasa N. Vempati, Washington University in Saint Louis
Abstract: For (X,d,w) be a space of homogeneous type in the sense of Coifman and Weiss, i.e. d is a quasi-metric on X and w is a positive measuresatisfying the doubling condition. Suppose that u and v are two locally finite positive Borel measures on (X,d,w ). Subject to the pair of weights satisfying a side condition, we characterize the boundedness of a Calderon--Zygmund operator T from L^{2}(u) to L^{2}(v) in terms of the A_{2} condition and two testing conditions. The proof uses stopping cubes and corona decompositions originating in work of Nazarov, Treil and Volberg, along with the pivotal side condition.
Host: John McCarthy