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Inequalities associated with dilations

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Title: Inequalities associated with dilations
Authors: Ozawa, Tohru Browse this author
Sasaki, Hironobu Browse this author
Keywords: Inequalities
Generator of semi-group of dilations
Sobolev's inequality
 Poincar´e's inequality
Hardy's inequality.
Issue Date: 2007
Publisher: Department of Mathematics, Hokkaido University
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 861
Start Page: 1
End Page: 12
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).
Type: bulletin (article)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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