Geodesic
Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 203-210

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If an increasing sequence $\{n_m\}$ of positive integers and a modulus of continuity $\omega$ satisfy the condition $\sum_{m=1}^\infty\omega(1/n_m)/m\infty$, then it is known that the subsequence of partial sums $S_{n_m}(f,x)$ converges almost everywhere to $f(x)$ for any function $f\in H_1^\omega$. We show that this sufficient convergence condition is close to a necessary condition for a lacunary sequence $\{n_m\}$.
Keywords: Fourier series, modulus of continuity.
Mots-clés : Lebesgue measure 
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     author = {S. V. Konyagin},
     title = {Almost everywhere divergence of lacunary subsequences of partial sums of {Fourier} series},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {203--210},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a18/}
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S. V. Konyagin. Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 203-210. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a18/