Inequalities associated with dilations

• Ozawa Tohru

• Sasaki Hironobu

Abstract

Some properties of distributions f satisfying x ¢ rf 2 Lp(Rn), 1 · p < 1, are studied. The operator x ¢ r is the generator of a semi-group of dilations. We first give Sobolev type inequalities with respect to the operator x ¢r. Using the inequalities, we also show that if f 2 Lp loc(Rn), x ¢rf 2 Lp(Rn) and jxjn=pjf(x)j 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).

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 861 1-12, 2007

  Department of Mathematics, Hokkaido University

Keywords

• Inequalities
• Generator of semi-group of dilations
• Sobolev's inequality
• Hardy's inequality.

Details

• CRID: 1390009224795399552
• NII Article ID: 120006459563
• DOI: 10.14943/84011
• HANDLE: 2115/69670
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed