On a nonclassical interpretation of the four-dimensional Goursat problem for one hyberbolic equation

A homeomorphism between certain pairs of Banach space is revealed in the study of the four-dimensional Goursat problem for one differential equation with leading partial derivative of the sixth order $D_{1} D_{2} D_{3}{2} D_{4}{2}$ with discontinuous coefficients ($L_p$-coefficients) by reducing this problem to an equivalent integral equation.