Extended Cesàro operators on mixed norm spaces

Abstract

We define an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of C n as T g (f)(z) = ∫ 1 0 f(tz)R g (tz)dt/t, f ∈ H(B), z ∈ B, where R g (z) = Σ n j=1 z j ∂ f /∂ zj 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 (ω).