A weighted Adams' inequality in ${\mathbb{R}}^4$ and applications

In this paper, we establish a weighted Adams’ inequality in some appropriate weighted Sobolev space in ${\mathbb{R}}^4$. Then we give an improvement inequality by proving the concentration-compactness result. In the last part, we consider an application to elliptic equation involving new exponential growth at infinity in ${\mathbb{R}}^4$.