Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem

The paper is concerned with estimates of the Hölder norms of solutions of model parabolic initial-boundary value problems in a half-space. The proof is based on the theorem on the Fourier multipliers in anisotropic Hölder spaces due to O. A. Ladyzhenskaya and on K. K. Golovkin's theorem on equivalent norms in these spaces.