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

Mikhail Dyachenko; Sergey Tikhonov

Studia Mathematica, Tome 192 (2009), p. 285-306 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2009-01-01

Zbl 1169.42001

EUDML-ID : urn:eudml:doc:284480

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Mikhail Dyachenko; Sergey Tikhonov. Integrability and continuity of functions represented by trigonometric series: coefficients criteria. Studia Mathematica, Tome 192 (2009) pp. 285-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-5/