Structure of solutions for the Lewy type equations (Q2367100)

Like of his earlier results about the reduction of the Mizohata equation to the Cauchy problem for the Cauchy-Riemann equations [\textit{H. Ninomiya}, J. Math. Kyoto Univ. 28, No. 4, 593-603 (1988; Zbl 0692.35026)], the author of the paper under the review shows that the same is valid for the H. Lewy equation. A comparison with the Grenier-Kohn- Stein local solvability conditions for the mentioned equation is given too [cf. \textit{P. C. Greiner}, \textit{J. J. Kohn} and \textit{E. M. Stein}, Proc. Natl. Acad. Sci. USA 72, 3287-3289 (1975; Zbl 0308.35017)]. The improvement obtained by the author explains the appearance of the Cauchy- Szegö kernel in solving the H. Lewy equation.