论文标题
具有Kato电势的非局部Schrödinger操作员的热内核
Heat kernels of non-local Schrödinger operators with Kato potentials
论文作者
论文摘要
我们研究了Schrödinger运算符的热核，其动力学项是非本地运算符，旨在进行足够规则的对称莱维措施，而径向减少的概况和电势属于Kato类。我们的设置相当一般和新颖 - 它使我们能够在关节框架中处理重型和轻尾的Lévy措施。我们为相应的半群和电势建立了一定的相对凯托。这使我们能够采用一般的扰动技术来构建热核并对其进行清晰的估计。假设Lévy测度和潜力满足了更强的条件，我们还获得了热核的规律性。最后，我们讨论了相应半群的平滑属性的应用。我们的结果涵盖了许多非本地运营商的重要例子，包括分数和准偏见的schrödinger运营商。
We study heat kernels of Schrödinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric Lévy measures with radial decreasing profiles and potentials belong to Kato class. Our setting is fairly general and novel -- it allows us to treat both heavy- and light-tailed Lévy measures in a joint framework. We establish a certain relative-Kato bound for the corresponding semigroups and potentials. This enables us to apply a general perturbation technique to construct the heat kernels and give sharp estimates of them. Assuming that the Lévy measure and the potential satisfy a little stronger conditions, we additionally obtain the regularity of the heat kernels. Finally, we discuss the applications to the smoothing properties of the corresponding semigroups. Our results cover many important examples of non-local operators, including fractional and quasi-relativistic Schrödinger operators.
