Geodesic
Fourier transform and continuity of functions of bounded $\Phi$-variation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 43-49.

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In this paper, we prove several criteria for the continuity of functions of bounded $\Phi$-variation that belong to the spaces $L^q$ on $\mathbb{R}$. The first result connects the continuity of a function with the behaviour of its Fourier transform, the second result is based on the notion of the modulus of continuity in $\Psi(L)$, and the third result concerns the degree of approximation by partial Fourier integrals. Theorems 1 and 3 in the case $\Phi(u)=|u|^p$, $1\le p\infty$, were obtained earlier by the first author.
Keywords: function of bounded $\Phi$-variation, continuity.
Mots-clés : Fourier transform 
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B. I. Golubov; S. S. Volosivets. Fourier transform and continuity of functions of bounded $\Phi$-variation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 43-49. http://geodesic.mathdoc.fr/item/INTO_2021_199_a4/

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