ON WEIGHTED SOLUTIONS OF $\overline{\partial}$-EQUATION IN THE UNIT DISC

Abstract

In the paper an equation $\partial g(z)/\partial \overline{z} = v(z)$ is considered in the unit disc $\mathbb{D}$.  For $C^k$-functions $v$ $(k = 1,2,3,\dots, \infty)$ from weighted $L^p$-classes $(1 \leq p < \infty)$ with weight functions of the type $|z|^{2\gamma} (1-|z|^{2\rho})^{\alpha}$, $z \in \mathbb{D}$, a family $g_{\beta}$ of solutions is constructed ($\beta$ is a complex parameter).