Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (4): 1489-1493.doi: 10.1016/S0252-9602(11)60334-2

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THE HARDY TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF THE ONE-DIMENSIONAL DYADIC DERIVATIVE

 Ushangi Goginava   

  1. Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze Str. 1, Tbilisi 0128, Georgia
  • Received:2009-04-02 Revised:2010-05-21 Online:2011-07-20 Published:2011-07-20

Abstract:

In this paper we prove that the maximal operator I* of dyadic derivative is not bounded from the Hardy space Hp [0, 1] to the Hardy space Hp [0, 1], when 0 < p  1.

Key words: Walsh function, Hardy space, dyadic derivative

CLC Number: 

  • 42C10
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