Directional maximal and singular integrals
Venue: Francesco Di Plinio - Aula Buzano (DISMA Politecnico di Torino)
This talk is concerned with L^p(R^n) estimates for maximal averaging operators on variable subspaces of codimension d between 1 and n-1, as well as their corresponding singular integral analogues. These estimates are related to the Kakeya and Nikodym maximal conjectures, to conical square function bounds and to Zygmund and Stein’s vector field conjectures. The focus will be on three results: a sharp estimate for directions belonging to an algebraic variety of fixed codimension, a codimension one estimate for maximal and square function operators, and a Lacey-Li codimension one vector field theorem. Joint work with I. Parissis and (partly) O. Bakas, L. Roncal.
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