Some Applications of Besov Spaces on Fractals

Let . be a compact d.set in .n with 0 < d . n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bspq(.)of Triebel and the Sobolev spaces W 1,p(., d, µ) of Haj.asz when s > 1, 1 < p < . and 0 < q . .. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces B0pq(.)and F0pq(.).