Bounded function on which infinite iterations of weighted berezin transform exist

초록

We exhibit some properties of the weighted Berezin transform T<inf>α</inf>f on L∞(B<inf>n</inf>) and on L1(B<inf>n</inf>). As the main result, we prove that if f ∈ L∞(B<inf>n</inf>) with exists, then there exist unique ℳ-harmonic function g and h ∈ such that f = g + h. We also show that of the norm of weighted Berezin operator T<inf>α</inf> on L1(B<inf>n</inf>,ν) converges to 1 as a tends to infinity, where v is an ordinary Lebesgue measure. © The Kangwon-Kyungki Mathematical Society, 2023.

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