Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (2): 375-382.doi: 10.1016/S0252-9602(15)60009-1

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THE SHARP JACKSON INEQUALITY FOR L2-APPROXIMATION ON THE PERIODIC CYLINDER

Yi GU1, Yongping LIU2   

  1. 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
    2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Received:2014-04-02 Revised:2014-07-01 Online:2015-03-20 Published:2015-03-20
  • Contact: Yongping LIU School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China E-mail: ypliu@bnu.edu.cn E-mail:ypliu@bnu.edu.cn
  • Supported by:

    This research was supported by National Natural Science Foundation of China (11071019), and Beijing Natural Science Foundation (1132001).

Abstract:

We consider Jackson inequality in L2(Bd×T,Wκ,μB (x)), where the weight function Wκ,μB (x)) is defined on the ball Bd and related to reflection group, and obtain the sharp Jackson inequality
En-1,m-1(f)2Kn,m(τ, r)ωr(f, t)2,τ≥2τn,λ,
where τn,λ is the first positive zero of the Gegenbauer cosine polynomial Cnλ(cosθ)(n∈N).d:\PDF\10.16381/j.cnki.issn1003-207x.2015.04.020.pdf

Key words: Jackson inequality, best approximation, modulus of continuity, weight function

CLC Number: 

  • 41A17
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