The concentration-compactness principle for the Trudinger–Moser-type inequality in the
Euclidean space was established crucially relying on the Pólya–Szegő inequality which …

Abstract Sharp Trudinger–Moser inequalities on the first order Sobolev spaces and their
analogous Adams inequalities on high order Sobolev spaces play an important role in …

Let H^ n= C^ n * RH n= C n× R be the n-dimensional Heisenberg group, Q= 2n+ 2 Q= 2 n+ 2
be the homogeneous dimension of H^ n H n. We extend the well-known concentration …

In this paper, we establish the existence of extremals for the Trudinger–Moser functional
under the weighted Sobolev norm involved with the trapping potential. Since the trapping …

Abstract Though the sharp Trudinger-Moser inequalities on compact Riemannian manifolds
have been known for some times, optimal constants for such inequalities on complete …

In this paper, we establish a sharp concentration-compactness principle associated with the
Trudinger–Moser inequality on Sobolev spaces with logarithmic weights. As applications …

The main purpose of this paper is to establish sharp weighted Trudinger–Moser inequalities
(Theorems 1.1, 1.2 and 1.3) and Caffarelli–Kohn–Nirenberg inequalities in the borderline …

The main purpose of this paper is to prove several sharp singular Trudinger–Moser-type
inequalities on domains in ℝ N with infinite volume on the Sobolev-type spaces DN, q⁢(ℝ …

Though much progress has been made with respect to the existence of extremals of the
critical first order Trudinger-Moser inequalities in W 1, n (R n) and higher order Adams …

The main purpose of this paper is three-fold. First of all, we will establish a weighted
Trudinger–Moser inequality on the entire space without requiring the functions under …