TY - JOUR
T1 - Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces
AU - Machihara, Shuji
AU - Ozawa, Tohru
AU - Wadade, Hidemitsu
PY - 2013/12
Y1 - 2013/12
N2 - 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.
AB - 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.
KW - Critical Sobolev-Lorentz space
KW - Logarithmic Hardy inequality
KW - O'Neil's inequality
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U2 - 10.1186/1029-242X-2013-381
DO - 10.1186/1029-242X-2013-381
M3 - Article
AN - SCOPUS:84894451210
SN - 1025-5834
VL - 2013
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
M1 - 381
ER -