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We prove local refined versions of Hardy's and Rellich's inequalities as wellas of uncertainty principles for sums of squares of vector fields on boundedsets of smooth manifolds under certain assumptions on the vector fields. Wealso give some explicit examples, in particular, for sums of squares of vectorfields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.

Local Hardy and Rellich inequalities for sums of squares of vector fields