Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states

In this paper, we investigate critical Gagliardo–Nirenberg, Trudinger-type and Brezis–Gallouet–Wainger inequalities associated with the positive Rockland operators on graded Lie groups, which include cases of [Formula: see text], Heisenberg, general stratified groups. As an application, using Gagliardo–Nirenberg inequality, existence least energy solutions nonlinear Schrödinger type equations is obtained. We also express best constant in Trudinger variational form as well terms ground state corresponding subelliptic equations. The obtained results are already new setting groups (homogeneous Carnot groups). Among technical methods, extend Folland’s analysis Hölder spaces from to homogeneous