FUNCTIONAL SPACES ASSOCIATED WITH THE WEYL-HORMANDER CALCULUS

Given a Hormander metric g on the phase space, we define for each weight function M a Hilbert space H(M, g) whose properties generalize those of the classical Sobolev spaces. We prove that invertible pseudo-differential operators of weight M exist for each M and we discuss relations between invertibility in the operator theorical sense and invertibility in the algebra of the pseudo-differential operators.