期刊论文详细信息
AIMS Mathematics | |
Function space properties of the Cauchy transform on the Sierpinski gasket | |
article | |
Songran Wang1  Zhinmin Wang3  | |
[1]Department of Mathematics, Shantou University | |
[2]College of Science, Central South University of Forestry and Technology | |
[3]School of Science, Hunan University of Technology | |
关键词: Cauchy transform; Sierpinski gasket; self-similar measure; Hardy space; multiplier; | |
DOI : 10.3934/math.2023306 | |
学科分类:地球科学(综合) | |
来源: AIMS Press | |
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【 摘 要 】
Let $ S_j(z) = \varepsilon_j +(z-\varepsilon_j)/2 $ be an iterated function system, where $ \varepsilon_j = e^{2j\pi i/3} $ for $ j = 0, 1, 2 $. Then, there exists a uniform self-similar measure $ \mu $ supported on a compact set $ K $, which is the attractor of $ \{S_j\}_{j = 0}^2 $. The Hausdorff dimension of the attractor $ K $ is $ \alpha = \log 3/\log 2 $. Let $ F(z) = \int_{K}(z-\omega)^{-1}d\mu(\omega) $ be the Cauchy transform of $ \mu $. In this paper, we consider the Hardy space and the multiplier property of $ F $. We prove that $ F' $ belongs to $ H^p $ for $ 0 < p < 1/(2-\alpha) $ and that $ F $ is a multiplier of some class of function space.【 授权许可】
CC BY
【 预 览 】
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