The singular anisotropic Adams' type inequality in $\mathbb{R}^n$

Abstract

In this paper, using anisotropic rearrangement techniques, we first establish the best constants for the singular anisotropic Adams' type inequality with exact growth in $\mathbb{R}^n$. Furthermore, by the same trick, we also prove the singular anisotropic Adams' type inequality on bounded domain $\Omega\subset \mathbb{R}^n$.