Log-Sobolev and Nash Inequalities on Graded Groups

In this work, we give a brief exposition of the results on important functional inequalities in the setting of graded Lie groups that appeared in the joint work Chatzakou et al. (Logarithmic Sobolev inequalities on Lie groups (2021). arXiv:2106.15652) with A. Kassymov and M. Ruzhansky. These inequalities include the logarithmic Sobolev inequality on graded groups, its semi-probabilistic equivalent on stratified groups, referred to as the “semi-Gaussian” logarithmic Sobolev inequality, and the Nash inequality on graded groups.