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The Weak Type (1,1) Estimates of Maximal Functions on the Laguerre Hypergroup

  Published:2010-06-11
 Printed: Sep 2010
  • Huang Jizheng,
    College of Sciences, North China University of Technology, Beijing 100144, China
  • Heping Liu,
    LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
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Abstract

In this paper, we discuss various maximal functions on the Laguerre hypergroup $\mathbf{K}$ including the heat maximal function, the Poisson maximal function, and the Hardy--Littlewood maximal function which is consistent with the structure of hypergroup of $\mathbf{K}$. We shall establish the weak type $(1,1)$ estimates for these maximal functions. The $L^p$ estimates for $p>1$ follow from the interpolation. Some applications are included.
Keywords: Laguerre hypergroup, maximal function, heat kernel, Poisson kernel Laguerre hypergroup, maximal function, heat kernel, Poisson kernel
MSC Classifications: 42B25, 43A62 show english descriptions Maximal functions, Littlewood-Paley theory
Hypergroups
42B25 - Maximal functions, Littlewood-Paley theory
43A62 - Hypergroups
 

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