| 概要 | The classical Hardy inequality is a weighted inequality for the lower order Sobolev space. On the other hand, the logarithmic Hardy type inequality is known for the critical Sobolev space. In this talk, we give a variant of the logarithmic Hardy inequality in terms of the critical Sobolev-Lorentz space. In particular, we can establish the logarithmic Hardy inequality for the weak critical Sobolev space. At the same time, we investigate the optimality for the exponents appearing in the inequality. This is a joint work with Professor Tohru Ozawa in Waseda University and Professor Shuji Machihara in Saitama University. |