Integrability and continuity of functions represented by trigonometric series: coefficients criteria
Volume 193 / 2009
Studia Mathematica 193 (2009), 285-306
MSC: Primary 42A16, 42A20; Secondary 41A17.
DOI: 10.4064/sm193-3-5
Abstract
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.
