arXiv subjects

Vít Musil

Publications and source records attributed to Vít Musil.

39 records · Page 3Linked to original sources

arXiv2017

Strict s-numbers of non-compact Sobolev embeddings into continuous functions

For limiting non-compact Sobolev embeddings into continuous functions we study behavior of Approximation, Gelfand, Kolmogorov, Bernstein and Isomorphism s-numbers. In the one dimensional case the exact values of the above-mentioned strict s-numbers were obtained and in the higher dimensions sharp estimates for asymptotic behavior of strict s-numbers were established. As all known results for s-numbers of Sobolev type embeddings are studied mainly under the compactness assumption then our work is an extension of existing results and reveal an interesting behavior of s-numbers in the limiting case when some of them (Approximation, Gelfand and Kolmogorov) have positive lower bound and others (Bernstein and Isomorphism) are decreasing to zero. From our results also follows that such limiting non-compact Sobolev embeddings are finitely strictly singular maps.

math.FA↗

arXiv2017

Optimal domain spaces in Orlicz-Sobolev embeddings

We deal with Orlicz-Sobolev embeddings in open subsets of $\mathbb{R}^n$. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces with respect to a Frostman measure, and, in particular, for trace embeddings on the boundary.

math.FA↗

arXiv2017

Strict s-numbers of the Volterra operator

For Volterra operator $V\colon L^1(0,1) \to C[0,1]$ and summation operator $σ\colon \ell^1 \to c$, we obtain exact values of Approximation, Gelfand, Kolmogorov, Mityagin and Isomorphism numbers.

math.FA↗