Optimal distribution estimates for commutators and Marcinkiewicz multipliers

Schedule

Weekday: Wednesday

Venue: A6-101

Zoom: 388 528 9728

Password: BIMSA

Organizers

Tadahisa Funaki

Professor

Jinsong Wu

Professor

Optimal distribution estimates for commutators and Marcinkiewicz multipliers

Fedor Sukochev

University of New South Wales

Speaker: Fedor Sukochev

Time: 17:00-18:30, Sep. 03, 2025

Abstract:

The main objective of this talk is to discuss the distributional estimates for (i) commutators with Calderón-Zygmund integral operators; (ii) Marcinkiewicz multipliers; (iii) Littlewood-Paley square function, via semigroup generated by Cesàro operator. In each of the cases (i)-(iii) we obtain new estimates of the distribution of elements in the range of the underlying operators in terms of the distribution function of the input function.

Our method allows us to obtain optimal estimates shedding additional light at the results due to Pérez (1995), Tao and Wright/Bakas et al. (2001/2024), Bourgain (1989). The main feature of the distributional form inequalities lies in its broad applicability across diverse problems in analysis, e.g. they allow obtaining estimates in wide range of symmetric quasi-Banach interpolation spaces between and (), not just for -spaces (). This is a joint work with Fulin Yang, Dmitriy Zanin and Dejian Zhou.

Speaker Intro:

Fedor Sukochev is a world leader in finding novel analytic approaches to complicated interdisciplinary problems. His research covers the area of mathematics inspired by quantum mechanics, where commuting variables are replaced by non-commuting ones. He is an internationally recognised expert in three related but distinct areas: noncommutative analysis; non-commutative geometry and; non-commutative probability.