Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (1): 373-386.doi: 10.1007/s10473-023-0121-8

Previous Articles     Next Articles


Zhuang Wang1, Haiqing Xu2,†   

  1. 1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
    2. Frontiers Science Center for Nonlinear Expectations (Ministry of Education of China), Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China
  • Received:2021-04-25 Revised:2022-06-14 Published:2023-03-01
  • Contact: †Haiqing XU. E-mail:
  • About author:Zhuang Wang,E-mail:
  • Supported by:
    *Young Scientist Program of the Ministry of Science and Technology of China (2021YFA1002200). The first author was supported by National Natural Science Foundation of China (12101226). The second author was supported by Shandong Provincial Natural Science Foundation (ZR2021QA032), and partially supported by the National Natural Science Foundation of China (12101362).

Abstract: Let $\mathbb{X}$ be a Jordan domain satisfying certain hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ in [A. Koski, J. Onninen, Sobolev homeomorphic extensions, J. Eur. Math. Soc. 23 (2021) 4065-4089, Theorem 3.1].

Key words: Poisson extension, Orlicz-Sobolev homeomorphisms, weighted Sobolev homeomorphisms, quasihyperbolic domains