论文标题
相对NASH类型和$ l^2 $ -sobolev的dunkl操作员和应用程序的不平等现象
Relative Nash-type and $L^2$-Sobolev inequalities for Dunkl operators and applications
论文作者
论文摘要
我们研究了DUNKL操作员的纳什不平等现象的本地变体。首先使用dunkl热核的梯度估计值确定了伪峰的不平等现象。这些不等式允许获得相对的NASH型不平等，这些不平等是为了获得平均值不平等，用于在球的轨道轨道上的亚物种，不一定以原点为中心。
We investigate local variants of Nash inequalities in the context of Dunkl operators. Pseudo-Poincaré inequalities are first established using pointwise gradient estimates of the Dunkl heat kernel. These inequalities allow to obtain relative Nash-type inequalities which are used to derive mean value inequalities for subsolutions of the heat equation on orbits of balls not necessarily centered on the origin.
