Abstract
In this paper, we introduce the weighted grand Lebesgue class \(h_{p);w}\) of harmonic function in unit ball \(\omega=\left\{z\in C:\,\left|z\right|<1\right\}\) on the complex plane \(C\) . It is established some properties of functions from theseclasses, when the weight function \(w:\partial\omega\to\bar{R}_{+}=\left[0,+\infty\right]\) satisfy the \(A_{p}\) Muckenhoupt condition. It is proved the unique solvability of theDirichlet problem for Laplace equation with an arbitrary boundaryvalue from weighted grand Lebesgue space \(L_{p);w}\left(\partial\omega\right)\) on \(\partial\omega\) .
