Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$

Details Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$ Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$

2007-08-02

arxiv.org/abs/0708.0269v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

In this paper, the sharp k-order Sobolev inequalities in the hyperbolic space
${\Bbb H}^n$ are established for all k=1,2,... . This solves a long-standing
open problem posed by Aubin [A${}_4$, p.176-177] for $W^{k,2}({\Bbb H}^n)$

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