【Coll.1018】Prof. Wen Yuan: Functional Calculus on BMO-type Spaces of Bourgain, Brezis and Mironescu

Speaker：  Professor Wen Yuan， 北京师范大学

Title：Functional Calculus  on BMO-type Spaces of Bourgain,  Brezis and  Mironescu

Abstract： A nonlinear superposition operator $T_g$ related to a Borel measurable function $g:\ {\mathbb C}\to {\mathbb C}$ is defined via $T_g(f):=g\circ f$ for any complex-valued function $f$ on ${\mathbb R^n}$. In this talk, we first recall some history of the study of superposition operators on various function spaces, and then introduce their behaviors on a new BMO type space recently introduced by Bourgain,  Brezis and  Mironescu [J. Eur. Math. Soc. (JEMS) 17 (2015),  2083-2101], as well as its VMO and CMO type subspaces.