Abstract
Following Wong's point of view, we construct the minimal and maximal extension in Lp (ℝ n ), 1 < p < ∞ for M-hypoelliptic pseudo-differential operators, which have been introduced and studied by Garello and Morando. We give some facts about the domain of minimal and maximal extensions of M-hypoelliptic pseudo-differential operators. For M-hypoelliptic pseudo-differential operators with constant coefficients, the spectrum and essential spectrum are computed.
Acknowledgements
The author is grateful to the referees for much valuable remarks and comments, which lead to several improvements of the first version of this article.