Korean J. Math.  Vol 28, No 3 (2020)  pp.449-457
DOI: https://doi.org/10.11568/kjm.2020.28.3.449

Iterates of weighted Berezin transform under invariant measure in the unit ball

Jaesung Lee


We focus on the interations of the weighted Berezin transform $T_{\alpha}$ on $L^{p}(\tau)$, where $\tau$ is the invariant measure on the complex unit ball $B_n$. Iterations of $T_{\alpha}$ on $L^{1}_{R}(\tau)$ the space of radial integrable functions played important roles in proving $\mathcal{M}$-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of $T_{\alpha}$ on $L^{1}_{R}(\tau)$ and observe differences between the iterations of $T_{\alpha}$ on  $L^{1}(\tau)$ and  $L^{p}(\tau)$ for $1<p<\infty$.


weighted Berezin transform, iteration, invariant measure, M-harmonic

Subject classification

Primary 32A70; Secondary 47G10


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