A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration

In this paper, we obtain a coercive a priori estimation of solutions to the boundary value problem in a half-space for a degenerate psedodifferential equation. The left part of the equation is the sum of the pseudo-differential operator with degeneracy, constructed by a special integral transformation, and the differentiation operator. A priori estimation is obtained in special weight spaces of the type of S. L. Sobolev spaces, the norms in which are constructed using a special integral transformation.