Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1623-1633.

• Articles • Previous Articles     Next Articles

(Cα)-summability of Character System of p}-series Field in Kaczmarz Rearrangement

  

  1. College of Science, Wuhan University of Science and Technology, |Wuhan 430065
  • Received:2008-06-05 Revised:2009-10-23 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    湖北省教育厅项目(B20081102)资助

Abstract:

Let Gp be the p-series field. G.Gát and K.Nagy[8] have shown that the maximal operator of the (C,1) means of the character system of the p-series filed in the Kaczmarz rearrangement is of type (q,q) for all 1<q ≤ ∞ and of weak type (1,1). In the present work the authors  extend these results to the (C, α) means where 0 < α ≤ 1 and prove
its maximal operator σ~α: Hp → Lp is bounded for all 1/(α+1) < p ≤ 1. By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, the $(C,\alpha)$ means of an integrable function f converge to f a.e..

Key words: p-series field, Kaczmarz rearrangement, Hardy-Lorentz space

CLC Number: 

  • 42C10
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