(untitled) (Journal of Partial Differential Equations, 2020)
In this note, we give a new proof of subcritical Trudinger-Moser inequality on R^n. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space W^1,n(R^n). Our method avoids this technique and thus can be used in the Riemannian manifold case and in the entire Heisenberg group.