ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 31C15,46E35,42B25 Edmunds, David E., Centre for Mathematical Analysis and Its Applications, University of Sussex, United Kingdom, Rákosník, Jiří, Mathematical Institute AS CR, Prague, Czech Republic On higher order Hardy inequality The Hardy inequality ∫_{Ω} |u(x)|^{p}d(x)^{−p}dx ≤ c ∫_{Ω} |∇u(x)|^{p}dx with d(x) = dist(x, ∂Ω) holds for u ∈ C_{0}^{∞}(Ω) if Ω ⊂ ℝ^{n} is an open set with a sufficiently smooth boundary and if 1 < p < ∞. P. Hajłasz 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.