A simple proof of the Adams type inequalities in $ {\mathbb R}^{2m} $

Van Hoang Nguyen

doi:10.3934/dcds.2020244

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2020, Volume 40, Issue 10: 5755-5764. Doi: 10.3934/dcds.2020244

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A simple proof of the Adams type inequalities in $ {\mathbb R}^{2m} $

Van Hoang Nguyen

Department of Mathematics, FPT University, Ha Noi, Vietnam

Received: July 2019

Revised: April 2020

Published: June 2020

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Abstract

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 $.

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Mathematics Subject Classification: Primary:46E35, 26D10;Secondary:35A23.

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