Approximation and entropy numbers in Besov spaces of generalized smoothness Original Research Article

We determine the exact asymptotic behaviour of entropy and approximation numbers of the limiting restriction operator image, defined by image. Here image is a non-empty bounded domain in image, image is an increasing slowly varying function, image, and image is the Besov space of generalized smoothness given by the function image. Our results improve and extend those established by Leopold [Embeddings and entropy numbers in Besov spaces of generalized smoothness, in: Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, Marcel Dekker, New York, 2000, pp. 323–336].