Limiting Embeddings for Sequence Spaces and Entropy Numbers
نویسنده
چکیده
The paper deals with embeddings for sequence spaces with general weights. Our main results are estimates for the entropy numbers of such compact embeddings in the non-limiting and the limiting case.
منابع مشابه
Entropy Numbers of Trudinger–strichartz Embeddings of Radial Besov Spaces and Applications
The asymptotic behaviour of entropy numbers of Trudinger–Strichartz embeddings of radial Besov spaces on Rn into exponential Orlicz spaces is calculated. Estimates of the entropy numbers as well as estimates of entropy numbers of Sobolev embeddings of radial Besov spaces are applied to spectral theory of certain pseudo-differential operators.
متن کاملSome limiting embeddings in weighted function spaces and related entropy numbers
The paper deals with weighted function spaces of type B p,q(R , w(x)) and F s p,q(R , w(x)), where w(x) is a weight function of at most polynomial growth. Of special interest are weight functions of type w(x) = (1 + |x|2)α/2 (log(2 + |x|))μ with α ≥ 0 and μ ∈ R. Our main result deals with estimates for the entropy numbers of compact embeddings between spaces of this type; more precisely, we may...
متن کاملLogarithmic Sobolev Spaces on R N ; Entropy Numbers, and Some Application 4 Applications 37 Logarithmic Sobolev Spaces on R N ; Entropy Numbers, and Some Application
In 14] and 11] we have studied compact embeddings of weighted function spaces on R n , p 2 (R n), s1 > s2, 1 < p1 p2 < 1, s1 ? n=p1 > s2 ? n=p2, and w(x) of the type w(x) = (1 + jxj) (log(2 + jxj)) , 0, 2 R. We have determined the asymptotic behaviour of the corresponding entropy numbers e k (idH). Now we are interested in the limiting case s1 ?n=p1 = s2 ?n=p2. of the so modiied embedding idH;a...
متن کاملEntropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights.∗
We study compact embeddings for weighted spaces of Besov and TriebelLizorkin type where the weights belong to Muckenhoupt Ap classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.
متن کاملPublications, Sorted by Subject
[4] D. Haroske. Some logarithmic function spaces, entropy numbers, applications to spectral theory. [9] D. Haroske and H. Triebel. Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators I. [10] D. Haroske and H. Triebel. Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential o...
متن کامل