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Title
Entropy numbers of embeddings of weighted Besov spaces. The limiting case.

Abstract
See here in pdf format

The talk presents results of joint work with T.Kühn (Leipzig), W. Sickel (Jena) and L. Skrzypczak (Poznan).

We investigate the asymptotic behaviour of the entropy numbers of the compact embedding

id:B^{s_1}_{p_1,q_1}(\R^d, w) -----> B^{s_2}_{p_2,q_2}\,(\R^d)

of the weighted Besov space B^{s_1}_{p_1,q_1}(\R^d, w) into the unweighted space B^{s_2}_{p_2,q_2}(\R^d). The weights which are admissible in our treatment are smooth, strictly positive, and satisfy

\lim_{|x|\to \infty} w(x)= \infty.

Most important for us will be the choice w_\alpha (x) = (1+ |x|^2)^{\alpha/2} for some \alpha >0. In the so called limiting situation, i.e.

\alpha = \big(s_1-\frac{d}{p_1}\big) - \big(s_2-\frac{d}{p_2}\big) > \max{\big(0,\frac{d}{p_2} - \frac{d}{p_1}\big)}

we give in almost all cases a sharp two-sided estimate.

Speaker(s)
Hans-Gerd Leopold (Friedrich-Schiller-University of Jena/Germany)

Date
September 24, 2004

Time
14h30

Room
Room 5.5

 
     
 

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