A1 Journal article (refereed)
Hardy spaces and quasiconformal maps in the Heisenberg group (2023)


Adamowicz, T., & Fässler, K. (2023). Hardy spaces and quasiconformal maps in the Heisenberg group. Journal of Functional Analysis, 284(6), Article 109832. https://doi.org/10.1016/j.jfa.2022.109832


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Publication details

All authors or editors: Adamowicz, Tomasz; Fässler, Katrin

Journal or series: Journal of Functional Analysis

ISSN: 0022-1236

eISSN: 1096-0783

Publication year: 2023

Volume: 284

Issue number: 6

Article number: 109832

Publisher: Elsevier

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jfa.2022.109832

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/84828

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2204.10016


Abstract

We define Hardy spaces Hp, 0 < p < ∞, for quasiconformal mappings on the Korányi unit ball B in the first Heisenberg group H1. Our definition is stated in terms of the Heisenberg polar coordinates introduced by Korányi and Reimann, and Balogh and Tyson. First, we prove the existence of p0 (K) > 0 such that every K-quasiconformal map f : B → f (B) ⊂ H1 belongs to Hp for all 0 < p < p0(K). Second, we give two equivalent conditions for the Hp membership of a quasiconformal map f , one in terms of the radial limits of f , and one using a nontangential maximal function of f . As an application, we characterize Carleson measures on B via integral inequalities for quasiconformal mappings on B and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from Rn to H1. A crucial difference between the proofs in Rn


Keywords: Hardy spaces; quasiconformal mappings

Free keywords: Heisenberg group; quasiconformal maps; Hardy spaces; Carleson measures


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Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 2


Last updated on 2024-03-04 at 19:37