Three examples of Sharp Commutator Estimates via Harmonic Extensions

Authors :: Armin Schikorra
Source :: Taiwanese J. Math. 23, no. 6 (2019), 1365-1388
Publication Year :: 2019
Publisher :: arXiv, 2019.
Abstract: Recently, Lenzmann and the author observed how to obtain a large class of sharp commutator estimates by a combination of an integration by parts, an harmonic extension, and trace space estimates. In this survey we review this approach in three concrete examples: the Jacobian estimate by Coifman-Lions-Meyer-Semmes, the Coifman-Rochberg-Weiss commutator estimate for Riesz transforms, and a Kato-Ponce-Vega-type inequality.<br />Comment: survey, accepted for publication: Taiwanese Journal of Mathematics