We prove some Hardy-type inequalities on half-spaces for Kohn's sub-Laplacian in the Heisenberg group. Furthermore, the constants we obtained are sharp.
We provide estimates on the degree of C l − G V -determinacy (G is one of Mather's groups R or K) of weighted homogeneous function germs which are defined on weighted homogeneous analytic variety V and satisfies a convenient Lojasiewicz condition. The result gives an explicit order such that the C l -geometrical structure of a weighted homogeneous polynomial function germ is preserved after higher order perturbations, which generalize the result on C l − K-determinacy of weighted homogeneous functions germs given by M.A.S. Ruas.
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