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

TL;DR

This paper establishes optimal constants for a class of anisotropic Adams' inequalities with singularities in both unbounded and bounded domains using rearrangement techniques.

Contribution

It introduces the first precise constants for singular anisotropic Adams' inequalities in alculus, extending the inequality to bounded domains.

Findings

Optimal constants for the inequalities are derived.

The inequalities are extended from alculus to bounded domains.

Rearrangement techniques are effectively used for proofs.

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