Geodesic
Sharp inequalities for the second modulus of continuity of periodic functions and of functions extended from the segment
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 33-49

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Sharp estimates for the deviation of some positive operators on the space of $2\pi$-periodic continuous functions are obtained in terms of the second modulus of continuity. The sharp constant in the problem of extending functions with preservation of the second modulus of continuity is found. Bibl. 5 titles. 
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     author = {O. L. Vinogradov},
     title = {Sharp inequalities for the second modulus of continuity of periodic functions and of functions extended from the segment},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--49},
     publisher = {mathdoc},
     volume = {232},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a2/}
}
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O. L. Vinogradov. Sharp inequalities for the second modulus of continuity of periodic functions and of functions extended from the segment. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 33-49. http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a2/