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Representation formulas and weighted Poincaré inequalities for Hörmander vector fields. (English) Zbl 0820.46026
Summary: We derive weighted Poincaré inequalities for vector fields which satisfy the Hörmander condition, including new results in the unweighted case. We also derive a new integral representation formula for a function in terms of the vector fields applied to the function. As a corollary of the $$L^ 1$$ versions of Poincaré’s inequality, we obtain relative isoperimetric inequalities.

##### MSC:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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##### References:
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