APPROXIMATION NUMBERS IN SOME WEIGHTED FUNCTION-SPACES

In this paper we study weighted function spaces of type B-p,q(s)(R(n), w(x)) and F-p,q(s)(R(n), w(x)) where w(x) is a weight function of at most polynomial growth, preferably w(x)=(1 + \x\(2))(alpha/2) with alpha is an element of R. The main result deals with estimates for the approximation numbers of compact embeddings between spaces of this type. Furthermore we are concerned with the dependence of the approximation numbers a, of compact embeddings between function spaces B-p,q(s)(Omega) and F-p,q(s)(Omega) on an underlying domain Omega. (C) 1995 Academic Press, Inc