Geodesic
The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 491-502

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DOI

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 fromthe interpolation. Some applications are included.
DOI : 10.4153/CMB-2010-058-6
Mots-clés : 42B25, 43A62, Laguerre hypergroup, maximal function, heat kernel, Poisson kernel 
Huang, Jizheng; Heping, Liu. The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 491-502. doi: 10.4153/CMB-2010-058-6
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     title = {The {Weak} {Type} (1, 1) {Estimates} of {Maximal} {Functions} on the {Laguerre} {Hypergroup}},
     journal = {Canadian mathematical bulletin},
     pages = {491--502},
     year = {2010},
     volume = {53},
     number = {3},
     doi = {10.4153/CMB-2010-058-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-058-6/}
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