Edmunds, D. E.; Haroske, D. Spaces of Lipschitz type, embeddings and entropy numbers. (English) Zbl 0932.46026 Diss. Math. 380, 43 p. (1999). The aim of the paper is twofold. First limiting embeddings of Besov spaces \(B^{1+{n\over p}}_{pq}(\mathbb{R}^n)\) and \(F^{1+{n\over p}}_{pq}(\mathbb{R}^n)\), with the fractional Sobolev spaces \(H^{1+{n\over p}}_p(\mathbb{R}^n)\) as a subclass, in \(\text{Lip}^{1,-\alpha}_p(\mathbb{R}^n)\) normed by \[ \|f|L_\infty(\mathbb{R}^n)\|+ \sup{|f(x)- f(y)|\over|x-y||\log|x-y||^\alpha},\quad \alpha>0, \] are considered. Sharp exponents \(\alpha\) in dependence on \(p\) and \(q\) are obtained (Theorem 2.1). Secondly, restricted to bounded domains the related embeddings (with exception of limiting cases) are compact. It is the second aim of the paper to estimate this compactness in terms of entropy numbers. Reviewer: H.Triebel (Jena) Cited in 1 ReviewCited in 17 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy 46E15 Banach spaces of continuous, differentiable or analytic functions Keywords:limiting embeddings; Besov spaces; fractional Sobolev spaces; compactness; entropy numbers PDFBibTeX XMLCite \textit{D. E. Edmunds} and \textit{D. Haroske}, Diss. Math. 380, 43 p. (1999; Zbl 0932.46026)