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Inequalities associated with dilations
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) |
URI: | http://hdl.handle.net/2115/69670 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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