论文标题
对同质群体上强硬型不平等的调查
A survey of Hardy type inequalities on homogeneous groups
论文作者
论文摘要
在这篇评论论文中，我们从Folland和Stein的同质群体的角度调查了Hardy类型的不平等现象。特别注意对分层群体的Hardy类型不平等，这给出了一类均匀的群体。在这种环境中，强硬类型不平等的理论与亚拉普拉斯次级基督的特性和更一般的下层偏微分方程都错综复杂地交织在一起。特别是，我们讨论了Badiale-Tarantello的猜想，并在Heisenberg组的半空间中对几何性不平等的猜想，并具有鲜明的常数。
In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.
