Weyl numbers of embeddings of tensor product Besov spaces

Abstract

In this paper we investigate the asymptotic behaviour of Weyl numbers of embeddings of tensor product Besov spaces into Lebesgue spaces. These results will be compared with the known behaviour of entropy numbers.

Gelfand numbers of embeddings of mixed Besov spaces

“…Now property (c) of the s-numbers together with part (iii) in Theorem 2.2 implies the estimate from above in the case p 1 , p 2 < 2 and t > The following proposition will be used to prove the results in Theorems 2.7 and 2.15, see [37,15]. for all n, m ∈ N.…”

“…However we can follow the proof there and obtain the similar result for Gelfand numbers. Concerning the estimate from above the main idea is using the decomposition method, see [43] and also [15]. We define the operators…”

“…First, the lower estimate follows from the relation x n ≤ c n , see (2.1). We refer to [15] for the behaviour of Weyl numbers of this embedding. Now we turn to estimate from above.…”

“…The lower estimate follow from the inequality x n ≤ c n . We refer again to [15,Theorem 3.4] for asymptotic behaviour of x n (App : S t p,p B(Ω) → L ∞ (Ω)). Let 1 < p < 2 and t > 1.…”

Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness

“…Note that in Corollary 7.8 the case p 0 = q 0 is excluded. In [29] Nguyen and Sickel studied Weyl numbers of embeddings of tensor product Besov spaces (p 0 = q 0 ) with small mixed smoothness into L p1 . Replacing x n by c n in the proof of [29,Lem.…”