Three examples of Sharp Commutator Estimates via Harmonic Extensions

2019/02/23 by Armin Schikorra, Schikorra, Armin
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.08778

openalex publication_date 2019/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Hörmander type multiplier theorem for multilinear operators

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