Geodesic
Estimates for functionals with a~known moment sequence in terms of deviations of Steklov type means
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 5-32

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Some estimates mentioned in the title are established. As implications, Jackson type inequalities with constants smaller than known previously are obtained. The results are valid in different spaces of periodic and non periodic functions. Bibl. 9 titles. 
@article{ZNSL_2010_383_a0,
     author = {O. L. Vinogradov and V. V. Zhuk},
     title = {Estimates for functionals with a~known moment sequence in terms of deviations of {Steklov} type means},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--32},
     publisher = {mathdoc},
     volume = {383},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a0/}
}
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O. L. Vinogradov; V. V. Zhuk. Estimates for functionals with a~known moment sequence in terms of deviations of Steklov type means. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a0/