On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

György Gát; Ushangi Goginava; Károly Nagy

doi:10.1556/sscmath.2009.1099

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 46: Issue 3

On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

Authors:

György Gát

György Gát College of Nyíregyháza Institute of Mathematics and Computer Science P.O. Box 166 Nyíregyháza H-4400 Hungary

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Ushangi Goginava

Ushangi Goginava Tbilisi State University Department of Mechanics and Mathematics Chavchavadze str. 1 Tbilisi 0128 Georgia

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, and

Károly Nagy

Károly Nagy College of Nyíregyháza Institute of Mathematics and Computer Science P.O. Box 166 Nyíregyháza H-4400 Hungary

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Pages:: 399–421

Online Publication Date:: 04 Jul 2009

Publication Date:: 01 Sep 2009

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.2009.1099

Keywords:: Primary 42C10; Walsh-Kaczmarz system; Marcinkiewicz-Fejér means; maximal operator

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The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H_pq into Lorentz space L_pq for every p > 2/3 and 0 < q ≦ ∞. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ_n ( f, x¹ , x² ) → ( x¹ , x² ) a.e. as n → ∞.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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