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Sobolev inequalities in disguise. (English) Zbl 0857.26006
We present a simple and direct proof of the equivalence of various functional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or subelliptic geometry, as well as on graphs and to certain non-local Sobolev norms. It only uses elementary cut-off arguments. This method has interesting consequences concerning Trudinger type inequalities.

MSC:
26D10 Inequalities involving derivatives and differential and integral operators
58D25 Equations in function spaces; evolution equations
31C15 Potentials and capacities on other spaces
39B72 Systems of functional equations and inequalities
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