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On the integral representation of superbiharmonic functions

Ali Abkar (2007)

Czechoslovak Mathematical Journal

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 an application we shall see that the polynomials are dense in weighted Bergman...

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