Multianisotropic integral operators defined by regular equations

The article continues the authors' previous research, where they are proved the well-posed solvability of regular equations in $\mathbb{R}^n$ and the Dirichlet problem in $\mathbb{R}_+^n$. We define a scale of weighted spaces in which the regular operators are correctly solvable. Approximate solutions to the corresponding Dirichlet problem are constructed with the use of integral operators.