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

Journal of inequalities and applications

Shuji Machihara¹ 

关键词: logarithmic Hardy inequality;    critical Sobolev-Lorentz space;    O’Neil’s inequality;   

DOI  :  10.1186/1029-242X-2013-381

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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. MSC:46E35, 26D10.

【 授权许可】

CC BY