Different degrees of non-compactness for optimal Sobolev embeddings

Autor:	Lang, Jan, Mihula, Zdeněk
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis 46E35 (Primary) 47B06 46B50 (Secondary)
Zdroj:	J. Funct. Anal., 284(10):109880, 2023
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jfa.2023.109880
Popis:	The structure of non-compactness of optimal Sobolev embeddings of $m$-th order into the class of Lebesgue spaces and into that of all rearrangement-invariant function spaces is quantitatively studied. Sharp two-sided estimates of Bernstein numbers of such embeddings are obtained. It is shown that, whereas the optimal Sobolev embedding within the class of Lebesgue spaces is finitely strictly singular, the optimal Sobolev embedding in the class of all rearrangement-invariant function spaces is not even strictly singular. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.07282 Zobrazit plný text záznamu View this record from Arxiv