  The orthogonality of Hilbert spaces whose elements can be represented as
simple and double layer potentials is determined. Conditions of well-posed
solvability of integral equations for the sum of simple and double layer
potentials equivalent to double-sided Dirichlet, Neumann, and Dirichlet-Neumann
boundary value problems for the Laplacian are established in the Hilbert space,
elements of which as well as their normal derivatives have the jump through
boundary surface. The properties of boundary operators that relate the
double-sided boundary conditions of different types for the three-dimensional
Laplace equation are investigated.
