Entropy Numbers of Embeddings of Weighted Besov Spaces
نویسندگان
چکیده
We investigate the asymptotic behavior of the entropy numbers of the compact embedding B1 p1,q1(R d , α) ↪→ B2 p2,q2(R ). Here Bs p,q (R d , α) denotes a weighted Besov space, where the weight is given by wα(x) = (1 + |x |2)α/2, and B2 p2,q2 (Rd ) denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of parameters: s2 < s1, 0 < p1, p2 ≤ ∞, and α = s1 − d p1 − s2 + d p2 > d max ( 0, 1 p2 − 1 p1 ) . In almost all cases we give a sharp two-sided estimate.
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