Pointwise Characterizations of Hardy-sobolev Functions
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چکیده
We establish pointwise characterizations of functions in the HardySobolev spaces H within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H(R) if and only if u ∈ L(R) and it satisfies the Hajlasz type condition |u(x)− u(y)| ≤ |x − y|(h(x) + h(y)), x, y ∈ R \ E, where E is a set of measure zero and h ∈ L(R). We also investigate HardySobolev spaces on subdomains and extend Hardy inequalities to the case p ≤ 1.
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تاریخ انتشار 2006