ABSTRACT

In this paper, generalized Bessel potential is studied. A generalization is achieved by considering the singular Laplace–Bessel operator instead of the Laplace operator in the construction of the Bessel potential. First, we give some auxiliary statements as weighted plane wave relation and generalized Bochner formula. Next, we consider the Bessel kernel and prove some of its properties. After that, we present the definition and properties of generalized Bessel potential. Finally, we consider the generalized Bessel potential as a solution to the singular screened Poisson equation.

中文翻译：

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广义贝塞尔势及其在非齐次奇异筛选泊松方程中的应用

摘要

本文研究了广义贝塞尔势。在贝塞尔势的构造中，通过考虑奇异的拉普拉斯-贝塞尔算子而不是拉普拉斯算子来实现泛化。首先，我们给出了一些辅助陈述，如加权平面波关系和广义 Bochner 公式。接下来，我们考虑 Bessel 核并证明它的一些性质。之后，我们给出了广义贝塞尔势的定义和性质。最后，我们将广义贝塞尔势视为奇异筛选泊松方程的解。