\(L^ p\)-differentiability of \(W^{l,p}(\mathbb{R}^ n)\quad (1<p<+\infty)\) functions (Q1369763)
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scientific article; zbMATH DE number 1077084
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^ p\)-differentiability of \(W^{l,p}(\mathbb{R}^ n)\quad (1<p<+\infty)\) functions |
scientific article; zbMATH DE number 1077084 |
Statements
\(L^ p\)-differentiability of \(W^{l,p}(\mathbb{R}^ n)\quad (1<p<+\infty)\) functions (English)
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20 April 1998
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The paper characterizes \(f\in W^\ell_p(\mathbb{R}^n)\), \(1<p<\infty\), in terms of \(f(x+ h)-f(x)- \sum^n_{j=1} h_jg_j\) with \(g_j\in L_p(\mathbb{R}^n)\) and \(f(x+ h)-\sum_{|\alpha|\leq \ell}{h^\alpha\over \alpha!} , g^\alpha(x)\), \(g^\alpha\in L_p(\mathbb{R}^n)\), where \(x\in \mathbb{R}^n\), \(h= (h_1,\dots, h_n)\in\mathbb{R}^n\).
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Sobolev spaces
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