Chronic 发表于 2025-3-25 03:22:44

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GAVEL 发表于 2025-3-25 09:09:32

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 ..

GEST 发表于 2025-3-25 14:28:00

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Solace 发表于 2025-3-25 16:39:14

Approximation of Functions of Several Variables and Imbedding Theorems

圆木可阻碍 发表于 2025-3-25 20:05:41

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optional 发表于 2025-3-26 01:48:29

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Finasteride 发表于 2025-3-26 07:34:14

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forestry 发表于 2025-3-26 10:27:36

Imbedding Theorems for Different Metrics and Dimensions,n .. As applied to the space ℝ. and to its coordinate subspace ℝ.(1 ≦ . ≦), this theorem reads:. ƒ ∈ .ℝ.) and (1) $$0{mathop<limits_=} varrho = l - {nover p}+{mover p^prime},1 {mathop<limits_=} p.<p^prime <infty,$$ P ? . (2) $$W_p^l({
m R}_n)
ightarrow W_{p^prime}^{lbrack varrho
brack}({
m R}

ALE 发表于 2025-3-26 13:15:34

Transitivity and Unimprovability of Imbedding Theorems. Compactness,)$ and numbers .′, .″, satisfying the inequalities (2) $$p_l{mathop<limits_=}{p^prime}<p^{primeprime}{mathop<limits_=} infty.$$ If the following conditions are satisfied : (3) $$varrho_i^prime = {r_ichiover chi_i},$$ (4) $$chi=1-{mathopsumlimits_{l=1}^n}{{1over p_l}-{1over p^prime}over r_l

具体 发表于 2025-3-26 18:33:13

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