The Weighted Grand Lebesgue Class of Harmonic Functions and the Dirichlet Problem

Abstract

In this paper, we introduce the weighted grand Lebesgue class h(p))(;w) of harmonic function in unit ball omega={z is an element of C:|z| (+)=[0,+infinity]satisfy the A(p) Muckenhoupt condition. It is proved the unique solvability of the Dirichlet problem for La place equation with an arbitrary boundary value from weighted grand Lebesgue space L-p);w(partial derivative omega)on partial derivative omega.