Extended Cesàro operators on mixed norm spaces

Hu, Zhangjian

doi:10.1090/S0002-9939-02-06777-1

Extended Cesàro operators on mixed norm spaces
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Proc. Amer. Math. Soc. 131 (2003), 2171-2179 Request permission

Abstract:

We define an extended Cesàro operator $T_g$ with holomorphic symbol $g$ in the unit ball $B$ of $C^n$ as \[ T_g(f)(z)=\int _0^1f(tz)\Re g(tz)\frac {dt}{t}, \qquad f\in H(B),z\in B, \] where $\Re g(z)= \sum _{j=1}^{n} z_j\frac {\partial f}{\partial z_j}$ is the radial derivative of $g$. In this paper we characterize those $g$ for which $T_g$ is bounded (or compact) on the mixed norm space $H_{p,q}(w)$.

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