Integrability and continuity of functions represented by
trigonometric series: coefficients criteria
Studia Mathematica, Tome 193 (2009) no. 3, pp. 285-306
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
study weighted p integrability infty trigonometric series shown integrability function weight alpha depends regularity conditions fourier coefficients criteria uniform convergence trigonometric series terms their coefficients studied
Affiliations des auteurs :
Mikhail Dyachenko 1 ; Sergey Tikhonov 2
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author = {Mikhail Dyachenko and Sergey Tikhonov},
title = {Integrability and continuity of functions represented by
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journal = {Studia Mathematica},
pages = {285--306},
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volume = {193},
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year = {2009},
doi = {10.4064/sm193-3-5},
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Mikhail Dyachenko; Sergey Tikhonov. Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Studia Mathematica, Tome 193 (2009) no. 3, pp. 285-306. doi: 10.4064/sm193-3-5
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