$M$-Ellipticity of Fredholm Pseudo-Differential Operators on $L^p({\mathbb{R}}^n)$ and Gårding'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 Gårding's inequality for $M$-elliptic operators and the hybrid class of pseudo-differential operators, namely SG$M$-elliptic operators.

arXiv comment19 pages