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In this paper, we consider a large class of critical problems with singular potentials on Carnot groups. In particular, we prove sharp regularity results in Marcinkiewicz spaces and the exact rate of decay of the solutions. Our general results apply, for instance, to the equation satisfied by the extremals of some relevant Hardy-Sobolev type inequalities on Stratified groups

L p -weak regularity and asymptotic behavior of solutions for critical equations with singular potentials on Carnot groups