2021/04/16 by Wang, Zhuang, Xu, Haiqing
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.07873
Let \mathbbX be a Jordan domain satisfying hyperbolic growth conditions. Assume that φ is a homeomorphism from the boundary ∂ \mathbbX of \mathbbX onto the unit circle. Denote by h the harmonic diffeomorphic extension of φ from \mathbbX onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h. These generalize the Sobolev regularity of h by Koski-Onninen [21, Theorem 3.1].