Szego Seminar: "Sufficient and necessary conditions for L^p boundedness of constant Haar multipliers"

Abstract: The collection of Haar functions on dyadic intervals forms an orthonormal basis in L^2(R). In this talk, we will introduce Haar multipliers and show a result by Katz and Pereyra that a constant Haar multiplier is bounded on L^p(R) for 1<p<\infity if and only if the symbols defining the Haar multiplier form a bounded sequence. Recent work in harmonic analysis has shown that it is possible to write any Calderon-Zygmund operator as an average of operators akin to the Haar multipliers. In this talk, we will also see how this result on constant Haar multipliers relates to L^p boundedness of the commutators between operators and functions of bounded mean oscillation with the help of paraproducts.

Host: Nathan Wagner