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 $\Omega \subset {\mathbb{R}}^n$.