Geodesic
Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32 
M. V. Babushkin; V. V. Zhuk. Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 31, Tome 445 (2016), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/
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     author = {M. V. Babushkin and V. V. Zhuk},
     title = {Growth of norms in $L_2$ of derivatives of {Steklov} functions and properties of functions defined by best approximations and {Fourier} coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--32},
     year = {2016},
     volume = {445},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_445_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the paper, for periodic functions, a connection between integrals of norms in $L_2$ of derivatives of Steklov functions and series constructed from Fourier coefficients and the best approximations in $L_2$ is established, and the question on their simultaneous convergence or divergence is considered. Similar investigations are carried out for even and odd periodic functions.

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