课程题目：Sharp differential/integral inequalities and the extreme functions
授课人：Prof. Meijun Zhu (University of Okhlahoma, USA)
In this series lectures, we shall start from the classical Hardy inequality to derive the Hardy-Littlewood inequality, which leads to Hardy-Littlewood’s conjecture, and late it becomes the famous Bliss lemma. Using this lemma, Talenti and Aubin derived the sharp Sobolev inequality. We will also cover Lieb’s sharp Hardy-Littlewood-Sobolev inequality, which yields another proof of sharp Sobolev inequality for without using Bliss lemma. I hope to cover Moser-Trudinger-Onofri inequality, as well as the classification of positive solutions to the differential/integral equations satisfied by the extreme functions to the mentioned sharp inequalities.