Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE BEREZIN TRANSFORM ON $D^n$

  • Lee, Jae-Sung (Topology and Geometry Research Center Kyungpook National University)
  • Published : 1997.04.01
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Abstract

We show that if $f \in L^{\infty}(D^n)$ satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of Berezin operator, then f is n-harmonic. And we give some remarks and a conjecture on the space $M_2={f \in L^2(D^2, m \times m)\midBf = f$.

Keywords

References

  1. J. Funct. Anal v.111 An invariant volume mean value property P. Ahern;M. flores;W. Rudin
  2. Spectral Theory and Complex Analysis J. P Ferrier
  3. Indiana U. Math. Journal v.24 Projections on spaces of holomorphic functions in balls F. Forelli;W. Rudin
  4. J. Funct. Anal v.68 On Power bounded operators . Katznelson;L. Tzafriri
  5. To appear An invariant mean value property in the polydisc J. Lee
  6. Function Theory in the unit Ball of $ C^n$ W. Rudin