Abstract
In this paper, we give analogues of local uncertainty inequality on
for stratified Laguerre hypergroup, connected with the spectral analysis of a given homogeneous sublaplacian
L
, also indicate how local uncertainty inequalities imply global uncertainty inequalities. It would be interesting to note that we deduce the local uncertainty inequalities for the radial functions on the Heisenberg group. Finally, we extend Heisenberg-Pauli-Weyl uncertainty inequality by ultracontractive properties of the semigroups generated by the differential operator and on the estimate on the heat kernel.