Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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BOUNDED FUNCTION ON WHICH INFINITE ITERATIONS OF WEIGHTED BEREZIN TRANSFORM EXIST

  • Jaesung Lee (Department of Mathematics, Sogang University)
  • Received : 2023.04.03
  • Accepted : 2023.09.05
  • Published : 2023.09.30
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Abstract

We exhibit some properties of the weighted Berezin transform Tαf on L∞(Bn) and on L1(Bn). As the main result, we prove that if f ∈ L∞(Bn) with limk→∞ Tkαf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator Tα on L1(Bn, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

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References

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