Bounded solutions of ellitpic equations as multipliers in spaces of differentiable functions

It is shown that bounded solutions of second order linear elliptic differential equations are multipliers in certain weighted Hilbert spaces or pairs of such spaces. The role of the weight is played by a power of the distance to the boundary of the domain or a function of the distance. This function is subjected to a condition which is necessary and sufficient for the solution to be in the corresponding class of multipliers.