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

• Autorzy: Mikhail Dyachenko , Sergey Tikhonov
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 3
• Strony: 285-306

Daty

wydano

2009

Twórcy

autor

Mikhail Dyachenko

• Moscow State University, Vorob'evy Gory, Moscow 119992, Russia

autor

Sergey Tikhonov

• ICREA and Centre de Recerca Matemática, Apartat 50, 08193 Bellaterra, Barcelona, Spain

Identyfikatory

DOI

10.4064/sm193-3-5