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Paper   IPM / M / 8314
School of Mathematics
  Title:   On the integral representation of superbiharmonic functions
  Author(s):  A. Abkar
  Status:   Published
  Journal: Czechoslovak Math. J.
  Vol.:  57
  Year:  2007
  Pages:   877-883
  Supported by:  IPM
We consider a nonnegative superbiharmonic function w satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for w in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions w satisfying the condition 0 ≤ w(z) ≤ C(1−|z|) in the unit disk. As in [1], we shall give an application in the theory of weighted Bergman spaces.

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