Anisotropic adams’ type inequality with exact growth in R4 ${\mathbb{R}}^{4}$

Abstract

In this paper, we mainly extend the classical Adams’ inequality to its anisotropic type. By using the rearrangement argument, we establish best constants for anisotropic Adams’ type inequality with exact growth in R4 ${\mathbb{R}}^{4}$ . We give the optimal growth rate of the exponential-type function in the whole space R4 ${\mathbb{R}}^{4}$ . Furthermore, using the same method, we also prove anisotropic Adams’ type inequality on bounded domain Ω⊂R4 ${\Omega}\subset {\mathbb{R}}^{4}$ .

Keywords

• anisotropic adams’ type inequality
• rearrangement
• exact growth
• 26d10
• 46e30
• 46e35