publication . Preprint . 2014

On the maximal operators of Riesz logarithmic means of Vilenkin-Fourier series

Tephnadze, George;
Open Access English
  • Published: 04 Oct 2014
Abstract
The main aim of this paper is to investigate $\left( H_{p},L_{p}\right) $ and $\left( H_{p},L_{p,\infty }\right) $ type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin-Fourier series.
Subjects
free text keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis, 42C10
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24 references, page 1 of 2

[1] G. N. AGAEV, N. Ya. VILENKIN, G. M. DZHAFARLY and A. I. RUBINSHTEIN, Multiplicative systems of functions and harmonic analysis on zero-dimensional groups, Baku, Ehim, 1981 (in Russian).

[2] I. BLAHOTA and G. GÁT, Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups, Anal. Theory Appl., 24 (2008), no. 1, 1-17. [OpenAIRE]

[3] I. BLAHOTA, G. GÁT and U. GOGINAVA, Maximal operators of Fejér means of Vilenkin-Fourier series. JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), 1-7.

[4] N. J. FUJII, A maximal inequality for H1 functions on the generalized Walsh-Paley group, Proc. Amer. Math. Soc. 77 (1979), lll-116.

[5] G. GÁT, Cesáro means of integrable functions with respect to unbounded Vilenkin systems, J. Approx. Theory 124 (2003), no. 1, 25-43.

[6] G. GÁT, Inverstigations of certain operators with respect to the Vilenkin systems, Acta Math. Hungar. N 1-2,61 (1993), 131-149.

[7] G. GÁT and K. NAGY, On the logarithmic summability of Fourier series, Georgian Math. J. 18 (2) (2011) 237-248.

[8] U. GOGINAVA, The maximal operator of Marcinkiewicz-Fejér means of the d-dimensional WalshFourier series. East J. Approx. 12 (2006), no. 3, 295-302.

[9] U. GOGINAVA, Maximal operators of Fejér-Walsh means. Acta Sci. Math. (Szeged) 74 (2008), no. 3-4, 615-624.

[10] U. GOGINAVA and K. NAGY, On the maximal operator of Walsh-Kaczmarz-Fejér means, Czechoslovak Math. J., 61 (136) (2011), 673-686.

[11] U. GOGINAVA, Maximal operators of Logarithmic means of one-dimensional Walsh-Fourier series, Rendiconti del Circilo Matematico di Palermo Serie II, 82(2010), pp. 345-357.

[12] J. PAL and P. SIMON, On a generalization of the comncept of derivate, Acta Math. Hungar., 29 (1977), 155-164.

[13] F. SCHIPP, Certain rearranngements of series in the Walsh series, Mat. Zametki, 18 (1975), 193-201.

[14] P. SIMON, F. WEISZ, Weak inequalities for Cesáro and Reisz summability of Walsh-Fourier series, J. Approx. Theory 151 (2008) 1-19.

[15] P. SIMON, Inverstigations with respect to the Vilenkin system, Annales Univ. Sci. Budapest Eotv., Sect. Math., 28 (1985) 87-101.

24 references, page 1 of 2
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