Czechoslovak Mathematical Journal

, Volume 65, Issue 4, pp 983–1002 | Cite as

On the Nörlund means of Vilenkin-Fourier series

  • István Blahota
  • Lars-Erik Persson
  • Giorgi Tephnadze
Article
First Online:
Received:

Abstract

We prove and discuss some new (H p ,L p )-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {q k : k ⩾ 0}. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results.

In the special cases of general Nörlund means t n with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence {q k : k ⩾ 0} in an appropriate way.

Keywords

Vilenkin system Vilenkin group Nörlund means martingale Hardy space maximal operator Vilenkin-Fourier series strong convergence inequality 

MSC 2010

42C10 42B25 
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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  • István Blahota
    • 1
  • Lars-Erik Persson
    • 2
    • 3
  • Giorgi Tephnadze
    • 4
    • 2
  1. 1.Institute of Mathematics and Computer SciencesCollege of NyíregyházaNyíregyházaHungary
  2. 2.Department Of Engineering Sciences and MathematicsLuleå University of TechnologyLuleåSweden
  3. 3.Narvik University CollegeNarvikNorway
  4. 4.Department of Mathematics, Faculty of Exact and Natural SciencesTbilisi State UniversityTbilisiGeorgia

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