2017
Том 69
№ 9

All Issues

Imbedding Theorems in Metric Spaces $L_{ψ}$

Agoshkova T. A.

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Abstract

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 $${L}_{\psi}\left({T}^m\right)=\left\{f\in {L}_0\left({T}^m\right):{\left\Vert f\right\Vert}_{\psi }:={\displaystyle {\int}_{T^m}\psi \left(\left|f(x)\right|\right)dx<\infty}\right\}.$$ The relationship between the modulus of continuity of functions from $L_{ψ} (T^m)$ and the corresponding $K$-functionals is analyzed and sufficient conditions for the imbedding of the classes of functions $H_{ψ}^{ω} (T^m)$ into $L_q (T^m),\; q ∈ (0; 1]$, are obtained.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 3, pp 323-335.

Citation Example: Agoshkova T. A. Imbedding Theorems in Metric Spaces $L_{ψ}$ // Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 291–301.

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