On multiplicators in Hölder spaces with nonhomogeneous metrics

In § 2 sufficient conditions of boundedness of the convolution operators with kernel $m$ in a nonhomogeneous Hölder space are given in terms of the Fourier-image of $m$. After that the result of § 2 are used to prove solvability in a Hölder space of the Cauchy problem for the linear systems of hydrodynamical type.