Composition Cesaro Operator on the Normal Weight Zygmund Space in High Dimensions Citation： Si XU,Xuejun ZHANG,Shenlian LI.Composition Cesaro Operator on the Normal Weight Zygmund Space in High Dimensions[J].Chinese Annals of Mathematics B,2021,42(1):69~84 Page view： 102        Net amount： 76 Authors： Si XU; Xuejun ZHANG;Shenlian LI Foundation： This work was supported by the National Natural Science Foundation of China (No.,11571104) and the Hunan Provincial Innovation Foundation for Postgraduate (No.,CX2018B286). Abstract： Let n>1 and B be the unit ball in n dimensions complex space bf C^{n}. Suppose that \varphi is a holomorphic self-map of B and \psi\in H(B) with \psi(0)=0. A kind of integral operator, composition Ces\{a}ro operator, is defined by T_{\varphi,\psi}(f)(z)=\int_{0}^{1}f[\varphi(tz)]R\psi(tz)\frac{\rmd t}{t}, \quad f\in H(B), \ z\in B.In this paper, the authors characterize the conditions that the composition Ces\{a}ro operator T_{\varphi, \psi} is bounded or compact on the normal weight Zygmund space \mathcal{Z}_{\mu}(B). At the same time, the sufficient and necessary conditions for all cases are given. Keywords： Normal weight Zygmund space, Composition Ces`aro operator,Boundedness and compactness Classification： 32A36, 47B38 Download PDF Full-Text