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.