On the fractional Laplace-Bessel operator

Abstract

<p>In this paper, we propose a novel approach to the fractional power of the Laplace-Bessel operator $ \Delta_{\nu} $, defined as</p><p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \Delta_{\nu} = \sum\limits_{i = 1}^{n}\frac{\partial^2}{\partial x_{i}^2} + \frac{\nu_i}{x_{i}}\frac{\partial}{\partial x_{i}}, \quad \nu_i\geq 0. $\end{document} </tex-math></disp-formula></p><p>The fractional power of this operator is introduced as a pseudo-differential operator through the multi-dimensional Bessel transform. Our primary contributions encompass a normalized singular integral representation, Bochner subordination, and intertwining relations.</p>