Minimal and maximal extensions of M-hypoelliptic proper uniform pseudo-differential operators in L\u3csup\u3ep\u3c/sup\u3e -spaces on non-compact manifolds

In the context of manifolds of bounded geometry, we show that the properties of proper uniform pseudo-differential operators (PUPDOs) constructed by Kordyukov, Meladze, and Shubin carry over to PUPDOs whose local representations have symbols belonging to the (weighted) class Mρ,Λm introduced by Garello and Morando. Under the M-ellipticity assumption, we show that the minimal and maximal extensions of such PUPDOs in the Lp-spaces, where 1 \u3c p\u3c ∞, coincide