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Analysis Mathematica

, Volume 14, Issue 2, pp 175–184 | Cite as

On Riesz means with respect to a cylindric distance function

  • Hajo Luers
Article

Keywords

Distance Function Cylindric Distance 
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О средних Рисса по цил индрической функции расстояния

Abstract

Рассматривается обо бщенный мультиплика тор суммирования по Рисс у вида (1−ϱ) + λ , гдеϱ — функция расст ояния наR n =R j ×R k , определенная соотно шениемϱ(ξ)=max{¦ξ 1¦, ¦ξ 1¦},ξ=(ξ 1,ξ 2),ξ 1R J ,ξ 2R k ,j,k≧1,n=j+k. В случаеn=3 доказанно, чт о (1−ϱ) + λ ∈[L 1(R n )]1, еслиλ>1/2; если жеj≳=4, то ф ункция (1−ϱ) + λ ни для какогоλR не есть мультипли катор наL p (R n ). если\(\left| {\frac{1}{p} - \frac{1}{{2}}} \right| \geqq \frac{{3}}{{2(n - 1)}}\).

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Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • Hajo Luers
    • 1
  1. 1.FB Mathematik Arbeitsgruppe 5Technische HochschuleDarmstadt

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