On the second moduli of continuity

  • S. V. Konyagin


We prove an inequality for the second moduli of continuity of continuous functions. Applying this inequality, we construct a nonnegative nonincreasing continuous function ω on [0, +g8) that vanishes at zero and is such that the function ω(δ)/δ 2 decreases on (0, +g8) while ω is not asymptotically (as δ → 0) equivalent to the second modulus of continuity of any continuous function.


Continuous Function Fourier Series STEKLOV Institute Wide Class Closed Interval 
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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • S. V. Konyagin
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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