广义Bergman空间上的紧复合算子

首先证明广义Bergman空间A_(N,α)~p,(α-n-1,p0)上的复合算子C_φ的有界性和紧性是不依赖于p的,进而证明了若对某个q0和-n-1βα,C_φ在A_(N,β)~α上有界,则C_φ在A_(N,α)~p,α(α-n-1,p0)上是紧的当且仅当lim|z|→1-1-(|z|~2/1-|φ(1)|~2)=0.

Compact Composition Operators on Generalized Bergman Spaces

We prove that the boundedness and compactness of the composition operators C_φ on generalized Bergman spaces A_N,α^p,(α>-n-1,p>0) are independent of p. On this foundation, we prove that if C_φ is bounded on A_N,β^p for some q> 0 and -n-1 < β < α, then C_φ is compact on A_N,α^p,(α>-n-1,p>0) if and only if lim_|z|→1-((1-|z|²)/(1-|φ(z)|²))=0.