Geodesic
On approximating periodic functions using linear approximation methods
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 134-164

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In the paper, a generalization of a known theorem by Hardy and Young is obtained; a formula interrelating the integral of a $2\pi$-periodic function over the period with the integral over the entire axis is established; new approximation characteristics for functions belonging to saturation classes of continuity modules of different orders for the spaces $L_p$ of periodic functions are provided, and some issues concerning approximation, in the uniform metric, of continuous periodic functions even with respect to each of their variables and having nonnegative Fourier coefficients are considered. Bibliography: 17 titles. 
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     author = {A. S. Zhuk and V. V. Zhuk},
     title = {On approximating periodic functions using linear approximation methods},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--164},
     publisher = {mathdoc},
     volume = {337},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a8/}
}
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A. S. Zhuk; V. V. Zhuk. On approximating periodic functions using linear approximation methods. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 134-164. http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a8/