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- W4313266963 abstract "<abstract><p>Let $ S_j(z) = varepsilon_j +(z-varepsilon_j)/2 $ be an iterated function system, where $ varepsilon_j = e^{2jpi 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}dmu(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.</p></abstract>" @default.
- W4313266963 created "2023-01-06" @default.
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- W4313266963 date "2022-01-01" @default.
- W4313266963 modified "2023-09-30" @default.
- W4313266963 title "Function space properties of the Cauchy transform on the Sierpinski gasket" @default.
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- W4313266963 doi "https://doi.org/10.3934/math.2023306" @default.
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