Inequalities associated with dilations

Tohru Ozawa, Hironobu Sasaki

研究成果: Article

8 引用 (Scopus)

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Some properties of distributions f satisfying x · ∇ f ∈ Lp (ℝn), 1 ≤ p < ∞, are studied. The operator x · ∇ is the generator of a semi-group of dilations. We first give Sobolev type inequalities with respect to the operator x · ∇. Using the inequalities, we also show that if $f \in L-\rm loc ^p (\mathbb R^n)$, x · ∇ f ∈ Lp (ℝn) and |x|n/p|f(x)| vanishes at infinity, then f belongs to Lp (ℝn). One of the Sobolev type inequalities is shown to be equivalent to the Hardy inequality in L2 (ℝn).

元の言語English
ページ(範囲)265-277
ページ数13
ジャーナルCommunications in Contemporary Mathematics
11
発行部数2
DOI
出版物ステータスPublished - 2009 4 1

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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