Abstract:The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined in domains of certain type to ordinary Nikolskii and Besov spaces of mixed smoothness in $ \mathbb R^d, $ that are function extension operators, thus incurring coincidence of both kinds of spaces in the said domains. It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which the theorems of those kind of extension have been derived. Under certain conditions, operators of partial differentiation from the aforementioned function spaces of mixed smoothness to Lebesgue spaces have been established to be continuous.
From: Sergey Kudryavtsev Mr. [view email]
[v1]
Mon, 11 Jan 2021 17:02:28 UTC (31 KB)
[v2]
Thu, 22 Apr 2021 05:46:37 UTC (31 KB)
[v3]
Thu, 4 May 2023 10:44:57 UTC (44 KB)
[v4]
Wed, 24 Jun 2026 16:44:09 UTC (44 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。