In this article we describe the novel method to construct fundamental
solutions for operators with variable coefficients. That method was introduced
in "A note on the fundamental solution for the Tricomi-type equation in the
hyperbolic domain"(J. Differential Equations,206(2004)227--252) to study the
Tricomi-type equation. More precisely, the new integral operator is suggested
which transforms the family of the fundamental solutions of the Cauchy problem
for the equation with the constant coefficients to the fundamental solutions
for the operators with variable coefficients
