DOI: 10.1515/ans-2023-0159 ISSN: 1536-1365

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

Tao Zhang, Fan Yang, Tingzhi Cheng, Chunqin Zhou
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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

R 4 ${\mathbb{R}}^{4}$
. We give the optimal growth rate of the exponential-type function in the whole space
R 4 ${\mathbb{R}}^{4}$
. Furthermore, using the same method, we also prove anisotropic Adams’ type inequality on bounded domain
Ω ⊂ R 4 ${\Omega}\subset {\mathbb{R}}^{4}$
.

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