Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces: REGULAR DISTANCES ON THE HEISENBERG GROUP
- NSF-PAR ID:
- 10033612
- Publisher / Repository:
- DOI PREFIX: 10.1112
- Date Published:
- Journal Name:
- Proceedings of the London Mathematical Society
- Volume:
- 115
- Issue:
- 2
- ISSN:
- 0024-6115
- Page Range / eLocation ID:
- 348 to 380
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We study commutators with the Riesz transforms on the Heisenberg group
. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms on$${\mathbb {H}}^{n}$$ among other settings.$${\mathbb {H}}^{n}$$