论文标题
尖锐对数sobolev不等式的平等案例的另一种方法
Another approach to the equality case of the sharp logarithmic Sobolev inequality
论文作者
论文摘要
在本说明中，我们表征了尖锐的$ l^2 $ -euclidean对数sobolev不平等的平等案例，并具有单一权重，从而利用了Bobkov和Ledoux \ cite {Bob}的想法。即使在未加权的情况下，我们的方法也是新的。另外，我们表明，相同的策略产生了平等案例的平等案例，即以$ 1 <p <\ intimary norm in $ {\ mathbb r}^n $的任意规范为$ 1 <p <\ infty $，如果不平等，则不平等。
In this note, we characterize the equality case of the sharp $L^2$-Euclidean logarithmic Sobolev inequality with monomial weights, exploiting the idea by Bobkov and Ledoux \cite{Bob}. Our approach is new even in the unweighted case. Also, we show that the same strategy yields the equality case of the sharp $L^p$-Euclidean logarithmic Sobolev inequality for $1 < p < \infty$ with arbitrary norm on ${\mathbb R}^n$, if the inequality is unweighted.
