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Extended Cesàro operators on mixed norm spaces

Authors:	Zhangjian Hu

Institution:	Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang, 313000, People's Republic of China --- and --- Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599

Abstract:	We define an extended Cesàro operator with holomorphic symbol in the unit ball of as $\begin{displaymath}T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{dt}{t}, \qquad f\in H(B),z\in B, \end{displaymath}$ where $\Re g(z)= \sum_{j=1}^{n} z_j\frac{\partial f}{\partial z_j}$ is the radial derivative of . In this paper we characterize those for which is bounded (or compact) on the mixed norm space $H_{p,q}(w)$ .

Keywords:	Ces\`{a}ro operator mixed norm space normal weight

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