Geodesic
Sharp inequalities for trigonometric polynomials with respect to integral functionals
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 38-53

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The problem on sharp inequalities for linear operators on the set of trigonometric polynomials with respect to integral functionals $\int_0^{2\pi}\varphi(|f(x)|)\,dx$ is discussed. A solution of the problem on trigonometric polynomials with given leading harmonic that deviate the least from zero with respect to such functionals over the set of all functions $\varphi$ determined, nonnegative, and nondecreasing on the semi-axis $[0,+\infty)$ is given.
Keywords: sharp inequalities for trigonometric polynomials, integral functional, trigonometric polynomials that deviate the least from zero. 
V. V. Arestov. Sharp inequalities for trigonometric polynomials with respect to integral functionals. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 38-53. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a3/
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