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| Paper IPM / M / 8314 |
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| Abstract: | |
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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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