$M$-Ellipticity of Fredholm Pseudo-Differential Operators on $L^p(\mathbb{R}^n)$ and G\r{a}rding's Inequality

Abstract

In this paper, we study the $M$-ellipticity of Fredholm pseudo-differential operators associated with weighted symbols on $L^p(\mathbb{R}^n)$, $1 < p < \infty$. We also prove the G\r{a}rding's inequality for $M$-elliptic operators and the hybrid class of pseudo-differential operators, namely SG$M$-elliptic operators.