MORE PROPERTIES OF WEIGHTED BEREZIN TRANSFORM IN THE UNIT BALL OF Cn

초록

We exhibit various properties of the weighted Berezin operator T<inf>α</inf> and its iteration Tk<inf>α</inf> on Lp (τ), where α > −1 and τ is the invariant measure on the complex unit ball B<inf>n</inf>. Iterations of T<inf>α</inf> on (formula presented) the space of radial integrable functions have performed important roles in proving M-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T<inf>α</inf> or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results. © The Kangwon-Kyungki Mathematical Society, 2022.

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