On a Higher-order Hardy Inequality
نویسندگان
چکیده
The Hardy inequality ∫ Ω |u(x)|pd(x)−p dx c ∫ Ω |∇u(x)|p dx with d(x) = dist(x, ∂Ω) holds for u ∈ C∞ 0 (Ω) if Ω ⊂ n is an open set with a sufficiently smooth boundary and if 1 < p < ∞. P.Haj lasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for p = 1.
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