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

Mikhail Dyachenko, and Sergey Tikhonov. "Integrability and continuity of functions represented by trigonometric series: coefficients criteria." Studia Mathematica 193.3 (2009): 285-306. <http://eudml.org/doc/284480>.

@article{MikhailDyachenko2009,
abstract = {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.},
author = {Mikhail Dyachenko, Sergey Tikhonov},
journal = {Studia Mathematica},
keywords = {trigonometric series; weighted integrability; uniform convergence; generally monotone sequences; trigonometric approximation},
language = {eng},
number = {3},
pages = {285-306},
title = {Integrability and continuity of functions represented by trigonometric series: coefficients criteria},
url = {http://eudml.org/doc/284480},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Mikhail Dyachenko
AU - Sergey Tikhonov
TI - Integrability and continuity of functions represented by trigonometric series: coefficients criteria
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 3
SP - 285
EP - 306
AB - 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.
LA - eng
KW - trigonometric series; weighted integrability; uniform convergence; generally monotone sequences; trigonometric approximation
UR - http://eudml.org/doc/284480
ER -