Norm constants in cases of the Caffarelli–Kohn–Nirenberg inequality

Akshay L. Chanillo, Sagun Chanillo and Ali Maalaoui

Vol. 292 (2018), No. 2, 293–303

DOI: 10.2140/pjm.2018.292.293

Abstract

Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli–Kohn–Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.

Keywords

Caffarelli–Kohn–Nirenberg inequality, weighted Sobolev inequality, quasiconformal maps, sharp constants, optimizers

Mathematical Subject Classification 2010

Primary: 46E35

Milestones

Received: 8 January 2017

Revised: 15 July 2017

Accepted: 15 July 2017

Published: 17 October 2017