Functions of Pseudo-Differential Operators of Non-positive Order

The aim of this paper is to define functions of several commuting and non-commuting self-adjoint pseudo-differential operators of non-positive order, by means of the H. Weyl formula[formula]Given 1<p<∞, the pseudo-differential operators under consideration belong to the Hörmander classLmρ, δ,m⩽−n(1−ρ|(1/p)−(1/2)|, 0<ρ⩽1, 0⩽δ<1,δ⩽ρand act on functions defined on the euclidean space Rn.