Minimal and maximal extensions of M-hypoelliptic proper uniform pseudo-differential operators in Lp-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 M ρ , Λ m introduced by Garello and Morando. Under the M-ellipticity assumption, we show that the minimal and maximal extensions of such PUPDOs in the L p -spaces, where 1 < p < ∞ , coincide. [ABSTRACT FROM AUTHOR]