A note on the Fourier coefficients and partial sums of Vilenkin-Fourier series

Abstract

The main aim of this paper is to investigate Paley type and Hardy-Littlewood type inequalities and strong convergence theorem of partial sums of Vilenkin-Fourier series.

arXiv commentVilenkin system, Fourier coefficients, partial sums, martingale Hardy space

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• On the Partial Sums and Marcinkiewicz and Fejér Means on the One- and Two-dimensional One-parameter Martingale Hardy Spaces
• Some new resuts on strong convergence of Fejér means with respect to Vilenkin systems
• Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series
• On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces