Cesàro means of integrable functions with respect to unbounded Vilenkin systems

Gát, György

doi:10.1016/s0021-9045(03)00075-3

Cited by 52 publications

(31 citation statements)

References 10 publications

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“…convergence of Fejér is due to Pál and Simon [11] (c.f. also [2]) for bounded Vilenkin series. Weisz [20] proved that the maximal operator of the Fejér means σ * is bounded from the Hardy space H 1/2 to the space weak-L 1/2 .…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 93%

A note on the maximal operators of Vilenkin—Nörlund means with non-increasing coefficients

Memić

Persson

Tephnadze

2016

Studia Scientiarum Mathematicarum Hungarica

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In [14] we investigated some Vilenkin-Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H 1/(1+α) to the space weak -L 1/(1+α) , (0 < α 1). In this paper we construct a martingale in the space H 1/(1+α) , which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin-Nörlund means with non-increasing coefficients are not bounded from the Hardy space H 1/(1+α) to the space L 1/(1+α) . In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

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