Imbedding Theorems in Metric Spaces $L_{ψ}$

• Date: 2014
• Main Authors: Agoshkova, T. A., Агошкова, Т. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2132
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $L_0 (T^m)$ be the set of periodic measurable real-valued functions of $m$ variables, let $ψ: R_+^1  → R_+^1$ be the continuity modulus, and let $${L}_{\psi}\left({T}^m\right)=\left\{f\in {L}_0\left({T}^m\right):{\left\Vert f\right\Vert}_{\psi }:={\displaystyle {\int}_{T^m}\psi \left(\left|f(x)\...