Ph.D Thesis Defense: "Weighted Inequalities on Spaces of Homogeneous Type"

Abstract: We will discuss the two weight inequalities for Calderon-Zygmund operators and commutators. We work in the setting of spaces of homogeneous type defined in the sense of Coifman and Weiss. Subject to the pair of weights u and v satisfying a side condition, we will show a characterization for 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. We will also give the two weight quantitative estimates for the commutator of maximal functions and the maximal commutators with respect to the symbol in weighted BMO space on spaces of homogeneous type and also provide the boundedness and compactness characterizations of the commutator of Calderon-Zygmund operators T.

Host: Brett Wick