Entropy Numbers in Weighted Function Spaces and Eigenvalue Distributions of Some Degenerate Pseudodifferential Operators I

Abstract

Abstract In this paper we study weighted function spaces of type B (ℝ n , Q ( x )) and F (ℝ n , Q ( x )), where Q(x) is a weight function of at most polynomial growth. Of special interest are the weight functions Q(x) = (1 + |x| 2 ) α/2 with α ϵ ℝ. The main result deals with estimates for the entropy numbers of compact embeddings between spaces of this type.