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Local Hardy and Rellich inequalities for sums of squares of vector fields. (English) Zbl 1373.35016

Summary: We prove local refined versions of Hardy’s and Rellich’s inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give some explicit examples, in particular, for sums of squares of vector fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.

MSC:

35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
35H20 Subelliptic equations
35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
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