$ L^p $ estimates for a class of degenerate operators

Abstract

<p style='text-indent:20px;'>We prove <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> estimates for the degenerate operator <inline-formula><tex-math id="M3">\begin{document}$ \mathcal L = \Delta +c\frac{y}{|y|^2}\cdot\nabla_y-\frac{b}{|y|^{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M4">\begin{document}$ L^p( \mathbb{R}^{N+M},\ |y|^c\,dx\,dy) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ 1&lt;p&lt;\infty $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ x\in \mathbb{R}^N,\ y\in \mathbb{R}^M $\end{document}</tex-math></inline-formula>.</p>