Geodesic
Proof of Schauder estimates for parabolic initial-boundary value model problems via O.\,A.~Ladyzhenskaya's Fourier multipliers theorem
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 133-156

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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. 
@article{ZNSL_2016_444_a7,
     author = {V. A. Solonnikov},
     title = {Proof of {Schauder} estimates for parabolic initial-boundary value model problems via {O.\,A.~Ladyzhenskaya's} {Fourier} multipliers theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--156},
     publisher = {mathdoc},
     volume = {444},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a7/}
}
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V. A. Solonnikov. Proof of Schauder estimates for parabolic initial-boundary value model problems via O.\,A.~Ladyzhenskaya's Fourier multipliers theorem. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 133-156. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a7/