Results in Mathematics

, Volume 39, Issue 3–4, pp 357–373 | Cite as

Equivalence of Integral Means

  • Tingfan Xie
  • Xinlong Zhou


Let Aρf and Lρf be the integral means of f on a ball and its sphere, respectively. Frequently they are regarded as a bridge because of the smoothness. In this paper we will investigate their equivalence. More precisely, we will prove, among others, the following relationship: for any 1 ≤ p ≤ ∞ and d ≥ 2,
$$\parallel A_\rho f-f\parallel _p\sim \parallel L_\rho f-f\parallel _p,\quad \forall f\in L^p({\rm R}^d).$$

AMS subject classifications

26A15 26B20 41A35 41A63 

Key Words

integral mean K-modulus iterates of operators Bessel function 


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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  1. 1.Department of Computer SciencceChina Institute of MetrologyHangzhouChina
  2. 2.Department of MathematicsUniversity of DuisburgDuisburgGermany

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