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Titlebook: Approximation of Functions of Several Variables and Imbedding Theorems; Sergei Mihailovic Nikol’skii Book 1975 Springer-Verlag • Berlin •

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The Function Classes ,, ,, , measurable function ƒ(.) = ƒ(., .). For fixed . it is a function of ., defined on the corresponding open one-dimensional set. If ƒ is absolutely continuous on any closed finite segment belonging to this set, then we will say that it is for the indicated . relative to ..
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Approximation of Functions of Several Variables and Imbedding Theorems
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Imbedding Theorems for Different Metrics and Dimensions,n [2].. As applied to the space ℝ. and to its coordinate subspace ℝ.(1 ≦ . ≦), this theorem reads:. ƒ ∈ .ℝ.) and (1) $$0{mathop
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Transitivity and Unimprovability of Imbedding Theorems. Compactness,)$ and numbers .′, .″, satisfying the inequalities (2) $$p_l {mathop
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