Реферат: Given a closed weakly regular d-thick subset S of ℝn, the existence of a bounded linear extension operator Ext: Tr|S (ℝ^n, \gamma) \to (ℝ^n, gamma) is proved for p \in (1, ∞), 0\leq d \leq n, r \in (max{1, n – d}, p), l \in N, and \gamma \in A_{p/r}(ℝ^n). In particular, it is proved that a linear bounded operator extension exists in the case where S is the closure of an arbitrary domain in ℝ^n, \gamma=1, and p > n – 1. The obtained results supplement those of previous studies, in which a similar problem was considered either in the case of p \in (n, ∞) without constraints on the set S or in the case of p \in (1, ∞) under stronger constraints on the set S.

Библиографическая ссылка: Vodop’yanov S.K. , Tyulenev A.I.
On the Whitney Problem for Weighted Sobolev Spaces
Doklady Mathematics. 2017. V.95. N2. P.1-5. DOI: 10.1134/S1064562417010276 WOS Scopus OpenAlex

Оригинальная: Водопьянов С.К. , Тюленев А.И.
О проблеме Уитни для весовых пространств Соболева
Доклады академии наук. 2017. Т.472. №6. С.634-638. DOI: 10.7868/S086956521706007X OpenAlex

Даты:

Поступила в редакцию:

23 сент. 2016 г.

Идентификаторы БД:

Web of science:	WOS:000399585800021
Scopus:	2-s2.0-85018521898
OpenAlex:	W2606723896

Цитирование в БД:

БД	Цитирований
Scopus	3
OpenAlex	6
Web of science	2

Альметрики: