论文标题
广义堕落的schrödinger操作员和耐寒空间的热内核
Heat kernels of generalized degenerate Schrödinger operators and Hardy spaces
论文作者
论文摘要
Let $\displaystyle L = -\frac{1}{w} \, \mathrm{div}(A \, \nabla u) + μ$ be the generalized degenerate Schrödinger operator in $L^2_w(\mathbb{R}^d)$ with $d\ge 3$ with suitable weight $w$ and measure $μ$.本文的主要目的是三倍。首先，我们获得了运营商$ L $的基本解决方案的上限。其次，我们证明了$ L $的热核的一些估计值，包括上限，Hölder连续性和比较估算值。最后，我们将结果应用于研究与操作员$ l $生成的关键功能相关的Hardy空间的最大功能表征。
Let $\displaystyle L = -\frac{1}{w} \, \mathrm{div}(A \, \nabla u) + μ$ be the generalized degenerate Schrödinger operator in $L^2_w(\mathbb{R}^d)$ with $d\ge 3$ with suitable weight $w$ and measure $μ$. The main aim of this paper is threefold. First, we obtain an upper bound for the fundamental solution of the operator $L$. Secondly, we prove some estimates for the heat kernel of $L$ including an upper bound, the Hölder continuity and a comparison estimate. Finally, we apply the results to study the maximal function characterization for the Hardy spaces associated to the critical function generated by the operator $L$.
