数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 359-370.doi: 10.1016/S0252-9602(16)30005-4

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WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

Ushangi GOGINAVA1, Károly NAGY2   

  1. 1. Department of Mechanics and Mathematics, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia;
    2. Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Sóstói str. 31/B, 4400 Nyíregyháza, Hungary
  • 收稿日期:2013-10-28 修回日期:2014-06-20 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:Ushangi GOGINAVA,E-mail:zazagoginava@gmail.com;Károly NAGY,E-mail:nkaroly@nyf.hu
  • 基金资助:

    The research was supported by project TÁMOP-4.2.2.A-11/1/KONV-2012-0051 and Shota Rustaveli National Science Foundation grant no.13/06 (Geometry of function spaces, interpolation and embedding theorems).

WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

Ushangi GOGINAVA1, Károly NAGY2   

  1. 1. Department of Mechanics and Mathematics, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia;
    2. Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Sóstói str. 31/B, 4400 Nyíregyháza, Hungary
  • Received:2013-10-28 Revised:2014-06-20 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    The research was supported by project TÁMOP-4.2.2.A-11/1/KONV-2012-0051 and Shota Rustaveli National Science Foundation grant no.13/06 (Geometry of function spaces, interpolation and embedding theorems).

摘要:

The main aim of this article is to prove that the maximal operator σ*κ of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to Walsh-Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.

关键词: Walsh-Kaczmarz system, Marcinkiewicz-Fejér means, Maximal operator, a.e. convergence, weak type inequality

Abstract:

The main aim of this article is to prove that the maximal operator σ*κ of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to Walsh-Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.

Key words: Walsh-Kaczmarz system, Marcinkiewicz-Fejér means, Maximal operator, a.e. convergence, weak type inequality

中图分类号: 

  • 42C10