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Results tagged with besov-spaces
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user 121665
5
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Accepted
Estimate of the difference quotients in terms of an $L^{1,\infty}$ function
The property (P) indeed characterizes the Sobolev space $W^{1,p}$.
Theorem 1. $f\in W^{1,p}(\mathbb{R}^n)$, $1<p\leq\infty$ if and only if $f\in L^p$ and there is $0\leq g\in L^p$ such that $$
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