Non local Poincaré inequalities on Lie groups with polynomial volume growth

الأصل · EN

Let G be a real connected Lie group with polynomial volume growth, endowed with its Haar measure dx. Given a C² positive function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a non-local Poincaré inequality on G with respect to M(x)dx.