Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MORE PROPERTIES OF WEIGHTED BEREZIN TRANSFORM IN THE UNIT BALL OF ℂn

  • Lee, Jaesung (Department of Mathematics, Sogang University)
  • Received : 2022.02.20
  • Accepted : 2022.07.25
  • Published : 2022.09.30
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Abstract

We exhibit various properties of the weighted Berezin operator Tα and its iteration Tkα on Lp(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball Bn. Iterations of Tα on L1R(𝜏) 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 Tα or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

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References

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