Abstract
The paper defines an extended Cesàro operator Tg with holomorphic symbol g in the unit ball B of Cn as Tg(f)(z)=∫01f(tz)ℜg(tz)dtt,f∈H(B),z∈B.Where ℜg(z)=∑zj∂g∂zj is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space B0.
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