Abstract
We prove the equivalence between analogs of the Paley and Nikol’skii inequalities for any orthonormal system of functions and for almost periodic polynomials with arbitrary spectrum.
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References
A. Zygmund, Trigonometric Series [Russian translation], Vol. 2, Mir, Moscow (1965).
M. F. Timan, “On one property of orthonormal systems satisfying the Nikol’skii inequality/’ in: Proceedings of the International Conference on the Theory of Approximation of Functions [in Russian], Nauka, Moscow, pp. 356–358.
S. M. Nikol’skii, “Inequalities for entire functions of finite degree and their application in the theory of differentiable functions of many variables,” Tr. Mat. Inst. Steklova, 38, 244–278 (1958).
B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1947).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1289–1292, September, 1998.
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Timan, M.F. On some inequalities for polynomials. Ukr Math J 50, 1473–1477 (1998). https://doi.org/10.1007/BF02525256
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DOI: https://doi.org/10.1007/BF02525256