Analysis Seminar: "An invitation to directional singular integrals"
Abstract: I will discuss two recent results obtained in collaboration with Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp L^2 estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions.
Host: Brett Wick