M\"obius invariant type function spaces

In1996, Professor Ruhan Zhao introduced a new notion of weighted actions by the M\"obius group on analytic functions on the unit disk indexed by apositive parameter $\alpha$ and proved that the $\alpha$-Bloch space is maximalamong all $\alpha$-M\"obius invariant function spaces. In this talk, weidentify the minimal non-trivial $\alpha$-M\"obius invariant functionspace and consider the existence and uniqueness of a non-trivial$\alpha$-M\"obius invariant quasi-Hilbert space of analytic functions onthe unit disk, which answer two questions raised by Professor Ruhan Zhao. Thetalk is based on a joint work with Professor Kehe Zhu.

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