Professor Galia Dafni,  Concordia University

Title: Boundedness and continuity of rearrangements in BMO and VMO

Abstract:

Joint work with Almut Burchard (Toronto) and Ryan Gibara (Cincinnati). Let \(f\) be a function of bounded mean oscillation (BMO) on cubes in \(\mathbb{R}^n\), \(n > 1\). If \(f\) is rearrangeable, we show that its symmetric decreasing rearrangement\(Sf\) belongs to \(\mathrm{BMO}(\mathbb{R}^n)\). We also improve the bounds for the decreasing rearrangement \(f^*\) by Bennett, DeVore and Sharpley, \(\|f^*\|_{ \mathrm{BMO}(\mathbb{R}_+)} \leq C_n\|f\| _{\mathrm{BMO}(\mathbb{R}^n)}\), by eliminating the exponential dependence of \(C_n\) on the dimension \(n\). The key is to switch from cubes to a comparable family of shapes. Using a family of rectangles that is preserved under bisections, one can prove a dimension-free Calder\'on-Zygmund decomposition, and the boundedness of the decreasing rearrangement with the same constant. Restricting to the subspace of functions of vanishing mean oscillation (VMO), we show that these rearrangements take VMO functions to VMO functions. Furthermore, while the map from \(f\) to \(f^*\) is not continuous in the BMO seminorm, we prove continuity when the limit is in VMO.

Please click here to register
*After registering, you will receive a confirmation email containing information about joining the meeting.

OIST-UT Joint talk series for future science-Season 5: Understanding of superorganisms: collective behavior, differentiation and social organization

Speaker: Samuel Creedon, City, University of London

Title: Defining an Affine Partition Algebra

Tuesday 9th November 2021, 16:00–17:00 JST (UTC+9), online on Zoom

Professor Denis Serre,  The UMPA

Title:  Compensated integrability: classical and singular Divergence-BV symmetric tensors

Abstract:

Compensated Integrability is a recent tool of Functional Analysis, which extends both the Gagliardo Inequality and the Isoperimetric Inequality. It concerns the determinant of positive symmetric tensors whose row-wise Divergence is controlled in the space of bounded measures. It is somehow dual to Brenier's Theorem of Optimal Transport. Its applications cover several domains in Mathematical Physics and in Differential Geometry.

CFF unit is pleased to invite you to the seminar.

Language: English

Prof. Tatiana Engel

Cold Spring Harbor Laboratory, Engel Laboratory, United States

https://facultyprofiles.cshl.edu/tatiana.engel

Zoom link: https://oist.zoom.us/j/98260915981?pwd=dWNFRVQrcUhCNWhrbGhtYWs0TEZPUT09

TQM unit is pleased to invite you to the seminar!

Faculty Lunctime Seminar.
Speaker: Eugene Kroll (STG).
Title: "Knocking Out Cancer's Sweet Tooth".