Geodesic
Some inequalities for trigonometric polynomials and Fourier coefficients
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 64-81

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The Bernstein inequalities for trigonometric polynomials are generalized. For the sums of Fourier coefficients, upper bounds with certain constants are obtained with respect to values that characterize the structural properties of functions. 
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     title = {Some inequalities for trigonometric polynomials and {Fourier} coefficients},
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V. V. Zhuk; G. Yu. Puerov. Some inequalities for trigonometric polynomials and Fourier coefficients. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 64-81. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a6/