Taiwanese Journal of Mathematics

Three Examples of Sharp Commutator Estimates via Harmonic Extensions

Armin Schikorra

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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.

Article information

Taiwanese J. Math., Volume 23, Number 6 (2019), 1365-1388.

Received: 6 July 2018
Revised: 22 February 2019
Accepted: 22 February 2019
First available in Project Euclid: 7 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B37: Harmonic analysis and PDE [See also 35-XX] 47B47: Commutators, derivations, elementary operators, etc.

commutator estimates BMO Hardy space


Schikorra, Armin. Three Examples of Sharp Commutator Estimates via Harmonic Extensions. Taiwanese J. Math. 23 (2019), no. 6, 1365--1388. doi:10.11650/tjm/190204. https://projecteuclid.org/euclid.twjm/1551927632

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