Hardy's inequalities for Sobolev functions

Juha Kinnunen, Olli Martio

Research output: Contribution to journalArticleScientificpeer-review

43 Citations (Scopus)


The fractional maximal function of the gradient gives a pointwise interpretation of Hardy's inequality for functions u ∈ W0 1,p(Ω). With mild assumptions on Ω Hardy's inequality holds for a function u ∈ W0 1,p(Ω) if and only if u ∈ W0 1,p(Ω).

Original languageEnglish
Pages (from-to)489-500
Number of pages12
JournalMathematical Research Letters
Issue number4
Publication statusPublished - 1997
MoE publication typeA1 Journal article-refereed


  • Capacity
  • Hardy inequality
  • Hölder continuity
  • Maximal function
  • Sobolev spaces

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