Carleson measures on domains in Heisenberg groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916398795587584 |
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| author | Adamowicz, Tomasz Gryszówka, Marcin |
| author_facet | Adamowicz, Tomasz Gryszówka, Marcin |
| contents | We study the Carleson measures on NTA and ADP domains in the Heisenberg groups $\mathbb{H}^n$ and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the $1$-quasiconformal family of mappings on the Korányi--Reimann unit ball. Moreover, we establish the $L^2$-bounds for the square function $S_α$ of a subelliptic harmonic function and the Carleson measure estimates for the BMO boundary data, both on NTA domains in $\mathbb{H}^n$. Finally, we prove a Fatou-type theorem on $(ε, δ)$-domains in $\mathbb{H}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Carleson measures on domains in Heisenberg groups Adamowicz, Tomasz Gryszówka, Marcin Analysis of PDEs Complex Variables Primary: 35H20, Secondary: 31B25, 42B37 We study the Carleson measures on NTA and ADP domains in the Heisenberg groups $\mathbb{H}^n$ and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the $1$-quasiconformal family of mappings on the Korányi--Reimann unit ball. Moreover, we establish the $L^2$-bounds for the square function $S_α$ of a subelliptic harmonic function and the Carleson measure estimates for the BMO boundary data, both on NTA domains in $\mathbb{H}^n$. Finally, we prove a Fatou-type theorem on $(ε, δ)$-domains in $\mathbb{H}^n$. |
| title | Carleson measures on domains in Heisenberg groups |
| topic | Analysis of PDEs Complex Variables Primary: 35H20, Secondary: 31B25, 42B37 |
| url | https://arxiv.org/abs/2409.01096 |