Carleson measures on domains in Heisenberg groups

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-06-22 DOI:10.1002/mana.12038

Tomasz Adamowicz, Marcin Gryszówka

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引用次数: 0

Abstract

We study the Carleson measures on nontangentially accessible (NTA) and admissible for the Dirichlet problem (ADP) domains in the Heisenberg groups $H^{n}$ 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 $H^{n}$ . Finally, we prove a Fatou-type theorem on $(ε, δ)$ -domains in $H^{n}$ . Our work generalizes results by Capogna–Garofalo and Jerison–Kenig.

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海森堡群域上的Carleson测度

我们研究了Heisenberg群H n $\mathbb {H}^n$中Dirichlet问题（ADP）域上的非切可及（NTA）和可容许（ADP）域上的Carleson测度，并给出了这些测度的两个表征：(1)亚椭圆调和函数的水平集，(2)通过Korányi-Reimann单位球上的1-拟共形映射族。此外，我们建立了次椭圆调和函数的平方函数S α $S_{\alpha }$的l2 $L^2$ -界和BMO边界数据的Carleson测度估计。都在H的NTA域$\mathbb {H}^n$。最后，我们证明了H n $\mathbb {H}^n$中（ε, δ） $(\varepsilon, \delta)$ -域上的一个fatou型定理。我们的工作推广了Capogna-Garofalo和Jerison-Kenig的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index