Imbedding Theorems in Metric Spaces $L_{ψ}$
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 $${L}_{\psi}\left({T}^m\right)=\left\{f\in {L}_0\left({T}^m\right):{\left\Vert f\right\Vert}_{\psi }:={\displaystyle {\int}_{T^m}\psi \left(\left|f(x)\...
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| Date: | 2014 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2132 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Let $L_0 (T^m)$ be the set of periodic measurable real-valued functions of $m$ variables, let $ψ: R_+^1 → R_+^1$ be the continuity modulus, and let
$${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)\right|\right)dx |
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