Abstract
In this paper, we are interested in the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. So, we consider the generalized shift operator, generated by the dual of the Laguerre hypergroup which topologically can be identified with the so-called Heisenberg fan, the subset of : by means of which fractional maximal function is investigated also the necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator on the dual of Laguerre hypergroup from the spaces to the spaces and from the spaces to the weak spaces is obtained.
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