Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces

Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

研究成果: Article査読

8 被引用数 (Scopus)

抄録

In this paper, we establish the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces. More precisely, we generalize the Hardy type inequality obtained in Edmunds and Triebel (Math. Nachr. 207:79-92, 1999). The generalized inequality allows us to take the exponents appearing in the inequality more flexibly, and its optimality is discussed in detail. O'Neil's inequality and its reverse play an essential role for the proof.

本文言語English
論文番号381
ジャーナルJournal of Inequalities and Applications
2013
DOI
出版ステータスPublished - 2013 12

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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