【和山数学论坛73讲】9月4日上午中山大学吴迪博士（后）学术报告

和山数学论坛第73讲


一、主 题：Sharp Bound for Hardy-Littlewood-Sobolev Inequality and Selberg's Integral Formula
二、主讲人：吴迪博士（后） 中山大学
三、时 间：2015年9月4日（周五上午）10:30—11:00
四、地 点：闻理园A4-305室

内容摘要：
In this talk, we investigate some necessary and sufficient conditions which ensure
validity of the Selberg's integral formula. That is, the Selberg's integral equation
$$\int_{\mathbb{R}^n}\prod\limits^k_{i=1}|x^i-t|^{-d_i}dt=C_{d_1,\cdots,d_k,n}\prod\limits_{1\le i Condition I is that $k=2$ and $\max\{d_1,d_2\} Condition II is that $k=3$, $\max\{d_1,d_2,d_3\} Actually, we completely answer the question raised by Grafakos in the reference
In fact, for some cases, the constant number $C_{d_1,\cdots,d_k,n}$ is just the sharp bound of the following Hardy-Littlewood Sobolevnequality$$\left|{\int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{f(x)g(y)}{|x|^\alpha|x-y|^\lambda|y|^\beta}dxdy}\right|\leC(p,q,\alpha,\lambda,\beta,n)\|f\|_{L^{p}(\mathbb{R}^n)}\|g\|_{L^{q}(\mathbb{R}^n)}.$$

理学院
应用数学研究所

2015年8月31日