Bers型空间和复合算子

For α∈（0,∞),let Hα^∞（or Hα^∞,0)denote the collection of all functions f which are analytic on the unit disc D and satisfy |f(z)|(1-|z|^2)^α=O(1)(or|f(z)|(1-|z|^2)^α=o(1) as |z|→1).Hα^∞,0)is called a Bers-type space (or a little Bers-type space).In this paper,we give some basic properties of Hα^∞，Cψ，the composition operator associated with a symbol function ψ which is an analytic self map of D,is difined by Cψf=f o ψ,We characterize the boundedness,and compactness of Cψ which sends one Bers-type space to another function space.     

COMPOSITION OPERATORS FROM B~a TO F(p,q,s)

Necessary and sufficient conditions are given for a composition operator Cof = f o o to be bounded and compact from Ba to F(p, q, s).     

COMPOSITION OPERATOR ON BERS-TYPE SPACES

Necessary and sufficient conditions are established for a composition operator C f = fo to be bounded or compact on the Bers-type space Ha and the little Bers-type space Ha The boundedness and compactness of the composition operator C on A() are characterized, which generalize the case of C on Ha.     

COMPOSITION OPERATORS FROM Bα TO F(p, q, s)

Necessary and sufficient conditions are given for a composition operator Cφ f ＝f o φ to be bounded and compact from Bα to F(p, q, s).