Håkan Hedenmalm: Weighted integrability of polyharmonic functions

Abstract. To address the uniqueness issues associated with the Dirichlet problem for the N-harmonic equationontheunitdisk D in the plane, we investigate the L^p ntegrability of N-harmonic functions with respect to the standard weight. (|1-|z|²)^\alpha. In particular if u is N-harmonic and the weighted integral of |u|^p is finite must then u be identically equal to 0.

For a detailed abstract and the full arcticle, see http://www.math.kth.se/~haakanh/publications/borichev-hedenmalm-AIM.pdf