学术报告（Luz Rocal 5.19）

摘要： We will consider maximal operators on $\mathbb{R}^n$ defined by taking arbitrary rotations of tensor products of an $(n-1)$-dimensional H\"ormander--Mihlin multiplier with the identity in one coordinate. These maximal operators are naturally connected to differentiation problems and maximally modulated singular integrals such as Sj\"olin's generalization of Carleson's maximal operator.

As the main result, we prove a weak-type $L^{2}(\mathbb{R}^n)$ estimate  on band-limited functions. As corollaries, we obtain a sharp $L^2(\mathbb{R}^n)$ estimate for the maximal operator restricted to a finite set of rotations in terms of the cardinality of the finite set and a version of the Carleson--Sj\"olin theorem. Our approach relies on higher dimensional time-frequency analysis elaborated according to the directional nature of the operator under study.

This is joint work with Odysseas Bakas, Francesco Di Plinio, and Ioannis Parissis.