We provide the simple proof of the Adams type inequalities in whole space $ {\mathbb R}^{2m} $. The main tools are the Fourier rearrangement technique introduced by Lenzmann and Sok [16], a Hardy–Rellich type inequality for radial functions, and the sharp Moser–Trudinger type inequalities in $ {\mathbb R}^2 $.

中文翻译：

---

关于Adams型不等式的简单证明 \ begin {document} $ {\ mathbb R} ^ {2m} $ \ end {document}

我们提供了整个空间$ {\ mathbb R} ^ {2m} $中亚当斯类型不等式的简单证明。主要工具是Lenzmann和Sok [16]，径向函数的Hardy-Rellich型不等式以及$ {\ mathbb R} ^ 2 $中的尖锐Moser-Trudinger型不等式。