Vilenkin-Fourier Coefficients and Partial Sums in Martingale Hardy Spaces

Lars-Erik Persson, George Tephnadze and Ferenc Weisz
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Lars-Erik Persson: UiT The Artic University of Norway
George Tephnadze: University of Georgia, School of Science and Technology
Ferenc Weisz: Eötvös Loránd University, Department of Numerical Analysis

Chapter Chapter 6 in Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series, 2022, pp 279-329 from Springer

Abstract: Abstract It is well-known that f ^ k → 0 , as k → ∞ for every f ∈ H 1 ( G m ) . $$\displaystyle \widehat {f}\left ( k\right )\rightarrow 0, \ \ \ \text{ as } \ \ \ k\rightarrow \infty \ \ \ \text{ for every } \ \ \ f\in H_{1}(G_m). $$ Actually, this holds also for all f ∈ L1(Gm) (see Lemma 1.8.2 ). The classical inequality of Hardy type is well known in the trigonometric as well as in the Vilenkin-Fourier analysis.

Date: 2022
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DOI: 10.1007/978-3-031-14459-2_6

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