Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (5): 1593-1602.doi: 10.1016/S0252-9602(14)60106-5

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APPROXIMATION BY WALSH-KACZMARZ-FEJÉR MEANS ON THE HARDY SPACE

George TEPHNADZE   

  1. Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Str. 1, Tbilisi 0128, Georgia; Department of Engineering Sciences and Mathematics, Lulea University of Technology, SE-971 87, Lulea, Sweden
  • Received:2012-12-07 Revised:2014-01-17 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    The research was supported by Shota Rustaveli National Science Foundation grant no.13/06 (Geometry of function spaces, interpolation and embedding theorems.

Abstract:

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej´er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0 < p ≤ 1/2.

Key words: Walsh-Kaczmarz system, Fejer means, martingale Hardy space, modulus of continuity

CLC Number: 

  • 42C10
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