M-Hypoelliptic pseudo-differential operators on L^p(ℝⁿ)

Abstract

Following Wong's point of view, we construct the minimal and maximal extension in L^p (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.

Keywords:

• M-hypoellipticity
• minimal and maximal pseudo-differential operators
• spectrum
• essential spectrum

Mathematical Subject Classifications (2000): :

• 47G30
• 35S05

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.