摘要
We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of Toeplitz operators.We first charactreize analytic symbolsφfor which the sequence Tφ*kf or Tφkf converges to 0 or∞as k→∞in norm for every nonzero Bergman function f.Also,we characterize analytic symbolsφfor which the norm of such a sequence is summable or not summable.We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.
作者
陈泳
Kei Ji IZUCHI
Kou Hei IZUCHI
Young Joo LEE
Yong CHEN;Kei Ji IZUCHI;Kou Hei IZUCHI;Young Joo LEE(Department of Mathematics,Hangzhou Normal University,Hangzhou 311121,China;Department of Mathematics,Niigata University,Niigata 950-2181,Japan;Department of Mathematics,Faculty of Education,Yamaguchi University,Yamaguchi 753-8511,Japan;Department of Mathematics,Chonnam National University,Gwangju 61186,Korea)
基金
supported by NSFC(11771401)
the last author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
