SOME RESULTS RELATED WITH POISSON-SZEG ¨O KERNEL AND BEREZIN TRANSFORM

Abstract

Let µ be a finite positive Borel measure on the unit ball B ⊂ Cn and ν be the Euclidean volume measure such that ν(B) = 1. For the unit sphere S = {z : |z| = 1}, σ is the rotation-invariant measure on S such that σ(S) = 1. Let P[f ] be the Poisson-Szeg¨o integral of f and ˜µ be the Berezin transform of µ. In this paper, we show that if there is a constant M > 0 such that

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