Abstract:In this paper, we partly solve the generalized Khavinson conjecture in the setting of hyperbolic harmonic mappings in Hardy space. Assume that u = P Ω [φ] and φ ∈ L p (∂Ω, R), where p ∈ [1, ∞], P Ω [φ] denotes the Poisson integral of φ with respect to the hyperbolic Laplacian operator ∆ h in Ω, and Ω denotes the unit ball B n or the half-space H n . For any x ∈ Ω and l ∈ S n−1 , let C Ω,q (x) and C Ω,q (x; l) denote the optimal numbers for the gradient estimateand gradient estimate in the direction lrespective… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.