On BMO and Carleson measures on Riemannian manifolds
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 2022
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| In: |
International mathematics research notices
Year: 2022, Issue: 2, Pages: 1245-1269 |
| ISSN: | 1687-0247 |
| DOI: | 10.1093/imrn/rnaa140 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1093/imrn/rnaa140
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| Author Notes: | Denis Brazke, Armin Schikorra, and Yannick Sire |
| Summary: | 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. |
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| Item Description: | Gesehen am 14.06.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1687-0247 |
| DOI: | 10.1093/imrn/rnaa140 |