Embeddings and entropy numbers in Besov spaces of generalized smoothness

The entropy numbers of embeddings of function spaces were used first in 1994 by Ed­ munds and Triebel to study the eigenvalue distributions of degenerate elliptic differential and pseudodifferential operators. For this reason exact estimates for the entropy numbers in many different cases are of special interest. Let Bsp q(Q) be the usual Besov space on a bounded domain Q in W l . Then the embedding

is compact if

Let ek be the corresponding entropy number. Then

This result was proved in its generality in 1989/92 by Edmunds and Triebel. ~ bk means, that there are positive constants c\ and cj such that c\ak < bk < C20* for all k 6 N.