On BMO and Carleson measures on Riemannian manifolds

• Verfasst von: Brazke, Denis [VerfasserIn]
• Verfasst von: Schikorra, Armin [VerfasserIn]
• Verfasst von: Sire, Yannick [VerfasserIn]
• Titel: On BMO and Carleson measures on Riemannian manifolds
• Verf.angabe: Denis Brazke, Armin Schikorra, and Yannick Sire
• E-Jahr: 2022
• Jahr: January 2022
• Umfang: 25 S.
• Fussnoten: Gesehen am 14.06.2022
• Titel Quelle: Enthalten in: International mathematics research notices
• Ort Quelle: Oxford : Oxford University Press, 1991
• Jahr Quelle: 2022
• Band/Heft Quelle: (2022), 2 vom: Jan., Seite 1245-1269
• ISSN Quelle: 1687-0247
• DOI: doi:10.1093/imrn/rnaa140
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1806912155

Abstract

Let $\mathcal{M}$ be a Riemannian $n$-manifold with a metric such that the manifold is Ahlfors regular. We also assume either non-negative Ricci curvature or the Ricci curvature is bounded from below together with a bound on the gradient of the heat kernel. We characterize BMO-functions $u: \mathcal{M} \to \mathbb{R}$ by a Carleson measure condition of their $\sigma $-harmonic extension $U: \mathcal{M} \times (0,\infty ) \to \mathbb{R}$. We make crucial use of a $T(b)$ theorem proved by Hofmann, Mitrea, Mitrea, and Morris. As an application, we show that the famous theorem of Coifman-Lions-Meyer-Semmes holds in this class of manifolds: Jacobians of $W^{1,n}$-maps from $\mathcal{M}$ to $\mathbb{R}^n$ can be estimated against BMO-functions, which now follows from the arguments for commutators recently proposed by Lenzmann and the 2nd-named author using only harmonic extensions, integration by parts, and trace space characterizations.