Hardy inequalities on homogeneous groups
报告人：Durvudkhan Suragan (Nazarbayev University)
地点：Room 1365, Sciences Building No. 1
Abstract: In this talk, we discuss Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. In short, our main idea is consistently working with relations of quasi-radial derivatives and the Euler operators, so from these relations follow various Hardy type inequalities with sharp constants on homogeneous groups. While describing the general theory of Hardy type inequalities in the setting of general homogeneous groups, we pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. To demonstrate applications of the theory we present solutions of two previously known conjectures. Particularly, we discuss the Badiale-Tarantello conjecture and the conjecture on the geometric Hardy inequality in a half-space on the Heisenberg group with a sharp constant. The present talk is partially based on our recent open access book (with the same title) with Michael Ruzhansky.