Solution of the Cauchy problem for a parabolic equation with singular coefficients

The paper is concerned with the Cauchy problem for the second order parabolic equation with the singular coefficients with respect to $t$ at the first order spatial derivatives. The solution of the problem is constructed in the explicit form. For it, it is defined a weighted Hölder space with the weight as a positive power of $t$. The existence, uniqueness, estimates of the solution are proved.