EMIS ELibM Electronic Journals
Vol. 37(51), pp. 89--92 (1985)

Previous Article

Next Article

Contents of this Issue

Other Issues


ELibM Journals

ELibM Home

EMIS Home

 

On the absolute summability of lacunary Fourier series

N.V. Patel and V.M. Shah

DM, Faculty of Science, University of Baroda, India

Abstract: 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 $\alpha$, $0<\alpha<1$, only at a point and when $\{n_k\}$ satisfies the gap condition $n_{k+1}-n_k\geq An_K^\beta k^\gamma$ ($0<\beta<1$, $\gamma\geq 0$) 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 (MSC2000): 42A28

Full text of the article:


Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition