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- Persson, Lars-Erik, et al.
(författare)
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A Note on Carleson-Hunt Type Theorems for Vilenkin-Fourier Series
- 2024
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Ingår i: Extended Abstracts 2021/2022. GMC 2021.. - : Birkhäuser Verlag. - 9783031485787 - 9783031485794 ; , s. 157-167
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Konferensbidrag (refereegranskat)abstract
- In this paper we discuss an analogy of the Carleson-Hunt theorem with respect to Vilenkin systems. In particular, we investigate the almost everywhere convergence of Vilenkin-Fourier series of f∈Lp(Gm) for p>1 in case the Vilenkin system is bounded. Moreover, we state an analogy of the Kolmogorov theorem for p=1 and construct a function f∈L1(Gm) such that the partial sums with respect to Vilenkin systems diverge everywhere.
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- Persson, Lars-Erik, et al.
(författare)
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An Analogy of the Carleson-Hunt Theorem with Respect to Vilenkin Systems
- 2022
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer. - 1069-5869 .- 1531-5851. ; 28:3
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss and prove an analogy of the Carleson-Hunt theorem with respect to Vilenkin systems. In particular, we use the theory of martingales and give a new and shorter proof of the almost everywhere convergence of Vilenkin-Fourier series of f is an element of L-p(G(m)) for p > 1 in case the Vilenkin system is bounded. Moreover, we also prove sharpness by stating an analogy of the Kolmogorov theorem for p = 1 and construct a function f is an element of L-1(G(m)) such that the partial sums with respect to Vilenkin systems diverge everywhere.
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