On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space

Abstract

The class of Poisson-Morrey harmonic functions in the unit circle is introduced, some properties of functions of this class are studied. Nontangential maximal function is considered and it is estimated from above via maximum operator, and the proof is carried out for the Poisson-Stieltjes integral, when the density belongs to the corresponding Morrey-Lebesgue space. The obtained results are applied to solving of the Dirichlet problem for the Laplace equation with the boundary value in Morrey-Lebesgue space.