2023/10/19 by David Kalaj, Kalaj, David · 3 citations
Mathematics · #Analytic and geometric function theory #Differential Equations and Boundary Problems #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2310.12643
Let K≥ 1 and p∈(1,2]. We obtain asymptotically sharp constant c(K,p), when K→ 1 in the inequality ‖\Im f‖p≤ c(K,p)‖\Re(f)‖p where f∈ hp is a K-quasiregular harmonic mapping in the unit disk belonging to the Hardy space hp, under the conditions arg(f(0))∈ (-π/(2p),π/(2p)) and f(\mathbbD)∩(-∞,0)=∅. The paper improves a recent result by Liu and Zhu in \citeaimzhu. We also extend this result for the quasiregular harmonic mappings in the unit ball in ℝn. We also extend Kolmogorov theorem for quasiregular harmonic mappings in the plane.