Recording: https://disk.pku.edu.cn/link/AAA3DF6541B79A4F8CBD632A51D18CD1F4
Valid Until: 2025-02-18 10:43
Abstract: Bourgain—Brezis inequalities is an informal name for a class of estimates that resemble the Sobolev embedding theorem and include the norms in the limit spaces L_1 or L_\infty. Those specific norms, one the one hand, make the inequalities harder to prove, and on the other hand, link them to problems in geometric measure theory. The phenomenon may be traced back to the work of Gagliardo and Nirenberg in late 50-s. It got an intensive development in the 2000-s motivated by a fresh insight by Bourgain and Brezis. Nowadays, the field gets its inspiration from connections to geometric measure theory. I will survey the field, draw the said connections, and, if time permits, outline the recent ``probabilistic’’ approach suggested by Ayoush, Wojciechowski, and me.
Bio: Dmitry Stolyarov is an outstanding expert in Functional Analysis. His research interests cover, in particular, Fourier Analysis, Bellman Functions, Banach Space Theory, and Regularized Traces. Dmitry graduated from the Faculty of Mathematics and Mechanics of Saint Petersburg State University at 2011. Three years later, he defended his PhD thesis devoted to Fourier Analysis and Embedding Theorems under supervision of Prof. S.V. Kislyakov. Now he works at the Faculty of Mathematics and Computer Science. Dmitry is a laureate of several prestigious awards and grants at national and international levels.
