Abstract
In this paper, we define an analog of the L (p) -L (q) Morgan's uncertainty principle for any exponential solvable Lie group G (p, q a [1,+a]). When G is nilpotent and has a noncompact center, the proof of such an analog is given for p, q a [2,+a], extending the earlier settings ([2], [4] and [5]). Such a result is only known for some particular restrictive cases so far. We also prove the result for general exponential Lie groups with nontrivial center.