Ismail Kombe
SHARP WEIGHTED RELLICH AND UNCERTAINTY PRINCIPLE 
INEQUALITIES ON CARNOT GROUPS
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ABSTRACT.  In this work we prove sharp weighted Rellich-type inequalities and their improved versions for general Carnot groups. To derive the improved Rellich-type inequalities we have established new weighted Hardy-type inequalities with remainder terms. We also prove new sharp forms of the weighted Hardy-Poincare and uncertainty principle inequalities for polarizable Carnot groups.