Geodesic
On the Absolute Summability of Lacunary Fourier Series
Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 89 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $f\in L[-\pi,\pi]$ and let its Foirer Series $\sigma(f)$ be lacynary. The absolute convergence of $\sigma(f)$ when $f$ satisfies Lipschitz condition of order $\alpha$, $0\alpha1$, only at a point and when $\{n_k\}$ satisfies the gap condition $n_{k+1}-n_k\geq An_K^\beta k^\gamma$ ($0\beta1$, $\gamma\geq 0$) is obtained by Patadian and Shah when $\alpha\beta+\alpha\gamma>(1-\beta)/2$. Here we study the absolute summability of $\sigma(f)$ when $\alpha\beta+\alpha\gamma\leq(1-\beta)/2$.
Classification : 42A28 
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     author = {N.V. Patel and V.M. Shah},
     title = {On the {Absolute} {Summability} of {Lacunary} {Fourier} {Series}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {89 },
     year = {1985},
     volume = {_N_S_37},
     number = {51},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a16/}
}
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N.V. Patel; V.M. Shah. On the Absolute Summability of Lacunary Fourier Series. Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 89 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a16/