@article{Wang2023, 
author = {Songran Wang and Zhinmin Wang},
title = {Function space properties of the Cauchy transform on the Sierpinski gasket},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6064-6073},
keywords = {Cauchy transform, Sierpinski gasket, self-similar measure, Hardy space, multiplier},
url = {https://www.sciopen.com/article/10.3934/math.2023306},
doi = {10.3934/math.2023306},
abstract = {Let        S    j    (  z  )  =      ε    j    +  (  z  −      ε    j    )      /    2 be an iterated function system, where        ε    j    =      e          2      j      π      i              /            3       for    j  =  0  ,  1  ,  2. Then, there exists a uniform self-similar measure    μ supported on a compact set    K, which is the attractor of    {      S    j        }          j      =      0        2  . The Hausdorff dimension of the attractor    K is    α  =  log  ⁡  3      /    log  ⁡  2. Let    F  (  z  )  =      ∫          K        (  z  −  ω      )          −      1        d  μ  (  ω  ) be the Cauchy transform of    μ. 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  −  α  ) and that    F is a multiplier of some class of function space.}
}