Iterates of a Berezin-type transform

作者：Liu Congwen^*

来源：Journal of Mathematical Analysis and Applications, 2007, 329(2): 822-829.

DOI：10.1016/j.jmaa.2006.07.018

• Berezin-type transform
• Mobius transformations
• infinite iteration
• Poisson extension

Let B be the open unit ball of R-n and dV denote the Lebesgue measure on R-n normalized so that the measure of B equals 1. Suppose f E is an element of L-1 (B, dV). The Berezin-type transform of f is defined by
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We prove that if f is an element of C((B) over bar) then the iterates B-k f Converge to the Poisson extension of the boundary values of f, as k -> infinity. This can be viewed as a higher dimensional generalization of a previous result obtained independently by Englis and Zhu.

• 出版日期2007-5-15
• 单位南开大学