An inequality for the third uniform moduli of continuity is proved. This inequality implies that an arbitrary 3-majorant is not necessarily a modulus of continuity of order 3.
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S. М. Nikol’skii, “Fourier series with given moduli of continuity,” Dokl. Akad. Nauk USSR, 52, No. 3, 191–194 (1946).
S. V. Konyagin, “On the second moduli of continuity,” in: Proc. Steklov Math. Institute, 269 (2010), pp. 1–3.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 10, pp. 1420–1424, October, 2014.
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Bezkryla, S.I., Nesterenko, O.N. & Chaikovs’kyi, A.V. On the Third Moduli of Continuity. Ukr Math J 66, 1589–1594 (2015). https://doi.org/10.1007/s11253-015-1034-z
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DOI: https://doi.org/10.1007/s11253-015-1034-z