Hardy inequalities with optimal constants and remainder terms ∗

نویسندگان

  • Filippo Gazzola
  • Hans-Christoph Grunau
چکیده

We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces W 1,p 0 and in higher-order Sobolev spaces on a bounded domain Ω ⊂ R can be refined by adding remainder terms which involve L norms. In the higher-order case further L norms with lower-order singular weights arise. The case 1 < p < 2 being more involved requires a different technique and is developed only in the space W 1,p 0 .

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تاریخ انتشار 2000