Some properties of the Berezin transform in the bidisc

초록

Let m be the Lebesgue measure on C normalized to m(D) = 1, μ be an invariant measure on D defined by dμ(z) = (1-|z|2)-2 dm(z). For f ∈ L1(Dn, m × · · · × m), Bf the Berezin transform of f is defined by,. We prove that if f ∈ L1(D2, μ×μ) is radial and satisfies, then for every bounded radial function l on D2 we have. Then, using the above property we prove n-harmonicity of bounded func- tion which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc. © 2017 Korean Mathematical Society.

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