On local solvability for a class of generalized Mizohata equations

Abstract

The image in C ∞ for a class of complex vector fields, containing the Mizohata operator, was characterized.Note that C is a linear partial differential operator of order ≤ 2m − 1, if P has order m. The result is the following:where p m and c 2m−1 represent the principal symbols of P and C, respectively.