Some Applications of Besov Spaces on Fractals

Let Γ be a compact d–set in ℝn with 0 < d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ B^{s}_{{pq}} (\Gamma ) $$\end{document}of Triebel and the Sobolev spaces W1,p(Γ, d, µ) of Hajłasz 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ B^{0}_{{pq}} (\Gamma ) $$\end{document}and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F^{0}_{{pq}} (\Gamma ). $$\end{document}