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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 4, Pages 203–210 (Mi timm654)  

Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series

S. V. Konyagin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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, Lebesgue measure, modulus of continuity.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 273, suppl. 1, S99–S106

Bibliographic databases:

Document Type: Article
UDC: 517.518.452
Received: 17.02.2010

Citation: S. V. Konyagin, “Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 203–210; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S99–S106

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