加权Bergman空间A_α~p上复合算子本质范数的定量估计

Quantitative estimate of essential norm of the composition operator on A_α~p

本文主要利用一般形式的Nevanlinna计数函数给出了加权Bergman空间上的复合算子本质范数的定量估计.特别地,得到了Hardy空间上复合算子本质范数的最佳下估计:||C_φ||_(e,Hp)~p≥im sup |a|→1 N_φ(a)/(-log|a|)另外,如果φ是内函数的话,则有||C_φ||_(e,Hp)~p≥im sup |a|→1 N_φ(a)/(-log|a|),1<p<∞.

In this paper, we get quantitative estimate of the essential norm of the composition operator Cφ on the weighted Bergman space Aα~p（D）（α -1,1≤p∞） in terms of the generalized Nevanlinna counting function. In particular, when α →-1, we find that on the Hardy space H^p（1 p ∞）, it holds that ｜｜Cφ｜｜（e,Hp）~p≥im sup ｜a｜→1 Nφ（a）/（-log｜a｜）.Moreover,if φ is an inner function, we have ｜｜Cφ｜｜（e,Hp）~p≥im sup ｜a｜→1 Nφ（a）/（-log｜a｜）,1 p ∞.