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

Abstract

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