On weighted classes of harmonic functions in the unit ball of Rn.

This article gives the main representation theorems for harmonic functions in the spaces bωp(B) on the unit ball B in R″. These spaces depend on a parameter function ω and are arbitrarily large. We receive the integral representation for the functions of bωp(B) over the unit ball. The article also gives a representation connected with the natural isometry between bω²(B) and the ordinary space L² on the unit sphere, which is explicitly given in the form of an integral operator along with its inversion. [ABSTRACT FROM AUTHOR]