The Cauchy problem for parabolic systems in anisotropic Zygmund spaces

The article deals with the Cauchy problem for a system of second-order parabolic equations with constant coefficients in weighted anisotropic Zygmund spaces. Estimates of the Poisson potential are established for such parabolic systems. The obtained result is used to construct a smoothness scale for solving the Cauchy problem for parabolic systems with zero right hand side in Zygmund spaces with weight.