Complex powers of a nonelliptic differential operator in L p-spaces

In the spaces L (p) = L (p) (a"e (n) ), we study complex powers of a nonelliptic differential operator D = I +Delta (x') represented in the form of partial acoustic potentials (in the variable x'). By using the method of approximative inverse operators, we construct the inversion of the potentials A (x) (gamma) ,phi with L (p) -densities and describe the image A (x) (gamma) ,(L (p) ) in terms of the inverting constructions.