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The talk presents results of joint work with T.KÌhn (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.
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