Abstract
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.
| Original language | English |
|---|---|
| Article number | 381 |
| Journal | Journal of Inequalities and Applications |
| Volume | 2013 |
| DOIs | |
| Publication status | Published - 2013 Dec 1 |
Keywords
- Critical Sobolev-Lorentz space
- Logarithmic Hardy inequality
- O'Neil's inequality
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Machihara, S., Ozawa, T., & Wadade, H. (2013). Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces. Journal of Inequalities and Applications, 2013, [381]. https://doi.org/10.1186/1029-242X-2013-381