Integrability and continuity of functions represented by trigonometric series: coefficients criteria

Tom 193 / 2009

Mikhail Dyachenko, Sergey Tikhonov Studia Mathematica 193 (2009), 285-306 MSC: Primary 42A16, 42A20; Secondary 41A17. DOI: 10.4064/sm193-3-5

Streszczenie

We study weighted $L_p$-integrability ($1\le p<\infty $) of trigonometric series. It is shown how the integrability of a function with weight $x^{-\alpha }$ depends on some regularity conditions on Fourier coefficients. Criteria for the uniform convergence of trigonometric series in terms of their coefficients are also studied.

Autorzy

  • Mikhail DyachenkoMoscow State University
    Vorob'evy Gory
    Moscow 119992, Russia
    e-mail
  • Sergey TikhonovICREA and Centre de Recerca Matemática
    Apartat 50
    08193 Bellaterra, Barcelona, Spain
    e-mail

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