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

Tom 193 / 2009

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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