Geodesic
Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 217-224

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We present a refinement of a theorem of V.A. Abilov, F.V. Abilova, and M.K. Kerimov on the exact constant in a Jackson type inequality between the mean-square approximation of a function of a complex variable by Fourier series in a system orthogonal in a bounded domain and the generalized modulus of continuity of order $m\geq 1$.
Keywords: generalized modulus of continuity, generalized translation operator, orthonormal system, Jackson-Stechkin inequality. 
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     author = {M. S. Saidusajnov},
     title = {Analysis of a theorem on the {Jackson-Stechkin} inequality in the {Bergman} space $B_2$},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a17/}
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M. S. Saidusajnov. Analysis of a theorem on the Jackson-Stechkin inequality in the Bergman space $B_2$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 217-224. http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a17/