About Approximation Numbers in Function Spaces

Abstract

Sharp estimates for the approximation numbers of embeddings between the function spaces B s pq and F s pq on domains are given in a case not thoroughly studied by Edmunds and Triebel. Corresponding sharp estimates are also obtained for the counterparts of that case in the weighted function space setting. Academic Press

Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights

“…3.3.3/2] was achieved in [10,Thm. 3.3.4] with the extension in [7]. In case of δ > n p * it reads as (4.18)…”

Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I

“…For convenience we recall the well known estimates of approximation numbers of embeddings of finitedimensional spaces, see [7,12,30].…”

On approximation numbers of Sobolev embeddings of weighted function spaces

“…We improve some earlier results obtained by Haroske and Caetano. However, the method we use is quite different from that one used in [11,3]; therefore we present further how it works in all cases. It is essentially the same method that was used for investigation of asymptotic behavior of entropy numbers of the embeddings; cf.…”

“…Later some of their estimates were improved by Caetano; cf. [3]. For weighted function spaces the counterpart of the theory was studied by Mynbaev and Otel'baev [20] in the case of fractional Sobolev spaces, and then more generally by Haroske, cf.…”