In this talk, we consider the problem: when M\"obius invariant function spaces are continuously embedded in tent spaces. It is known as Carleson measure problem. We will introduce the recent development of Carleson measure for some well-known analytic function spaces， and present our work on Carleson measure for $BMOA$, Bloch space, $Q_p$ spaces, $Z_p$ spaces and Dirichlet space.

Add:Building 58, The School of Mathematics, Tianjin University Beiyangyuan Campus,

No. 135, Ya Guan Road, Jinnan District, Tianjin, PRC

Tel:022-60787827 Mail:math@tju.edu.cn