Geodesic
On Maximal Function on the Laguerre Hypergroup
Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 307-318.

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Let K = [0, ∞)×R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we consider the generalized shift operator, generated by Laguerre hypergroup, by means of which the maximal function is investigated. For 1 p ≤ ∞ the Lp(K)-boundedness and weak L1(K)-boundedness result for the maximal function is obtained.
Keywords: Laguerre Hypergroup, Generalized Translation Operator, Fourier-Laguerre Transform, Maximal Function 
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Guliyev, Vagif; Assal, Miloud. On Maximal Function on the Laguerre Hypergroup. Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 307-318. http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a6/