Hypoelliptic functional inequalities

摘要: In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained include Hardy, Rellich, Hardy-Littllewood-Sobolev, Galiardo-Nirenberg, Caffarelli-Kohn-Nirenberg and Trudinger-Moser inequalities. Some these estimates have been known in the case sub-Laplacians, however, more almost all them appear to be new as no approaches obtaining such available. Moreover, obtain several versions local global weighted with remainder terms, critical Hardy Gagliardo-Nirenberg inequalities, which also sub-Laplacian. Curiously, show equivalence many well asymptotic relations between their best constants. approach developed relies establishing integral groups, find necessary sufficient conditions weights true. Consequently, link different by using Riesz Bessel kernels associated described operators.