Vol. 292, No. 2, 2018

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ISSN: 0030-8730
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
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
Authors
Akshay L. Chanillo
Skillman, NJ
United States
Sagun Chanillo
Department of Mathematics
Rutgers University
Piscataway, NJ
United States
Ali Maalaoui
Department of mathematics and natural sciences
American University of Ras Al Khaimah
Ras Al Khaimah
United Arab Emirates