论文标题
一个扩展问题，Trace Hardy和Hardy对Ornstein-Uhlenbeck操作员的不平等现象
An extension problem, trace Hardy and Hardy's inequalities for Ornstein-Uhlenbeck operator
论文作者
论文摘要
在本文中，我们研究了Ornstein-uhlenbeck操作员的扩展问题$ l =-Δ +2x \ cdot \ nabla +n $，我们获得了相同溶液的各种特征。我们使用该扩展问题的特定解决方案来证明$ l $的痕迹不平等，从中获得了Hardy对$ L $的分数权力的不平等。我们还证明了与扩展问题关联的解决方案运算符的等轴测属性。此外，还为HERMITE操作员的分数功率获得了新的$ L^p-l^Q $估计。
In this paper, we study an extension problem for the Ornstein-Uhlenbeck operator $L=-Δ+2x\cdot\nabla +n$ and we obtain various characterisations of the solution of the same. We use a particular solution of that extension problem to prove a trace Hardy inequality for $L$ from which Hardy's inequality for fractional powers of $L$ is obtained. We also prove an isometry property of the solution operator associated to the extension problem. Moreover, new $L^p-L^q$ estimates are obtained for the fractional powers of the Hermite operator.
