Geodesic
Fourier series of functions with a non-summable derivative
Izvestiya. Mathematics, Tome 73 (2009) no. 2, pp. 301-318 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the convergence of Fourier series in the norm of Orlicz spaces narrower than $L(e^x)$. It is shown that if a continuous function has a non-summable derivative, then its Fourier series is not necessarily convergent in the norm of these Orlicz spaces. We find a condition on a bounded function $f$ under which the Fourier series of $f$ is convergent in the norm of an Orlicz space $L(\varphi)\subset L(e^x)$ and estimate the accuracy of this result.
Keywords: Fourier series, Lorentz spaces, local modulus of continuity.
Mots-clés : convergence 
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S. F. Lukomskii. Fourier series of functions with a non-summable derivative. Izvestiya. Mathematics, Tome 73 (2009) no. 2, pp. 301-318. http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a2/

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