On some Hilbert spaces of harmonic functions

Abstract

Two kinds of spaces of harmonic functions defined on m-dimensional domains are considered. In the first case, the spherical domain is a m-dimensional ball B_r in the second case B_r is replaced by B_r1,r2:=B_r2B_r1. In both cases, several inner products are considered and Hilbert space properties are proved. The reproducing kernel functions of these spaces and hence some new representations for harmonic functions are also obtained