A representation theorem for standard weighted harmonic mappings with an integer exponent and its applications.

In this paper, we study α ¯ -harmonic mappings with an integer exponent and obtain a representation theorem which determines the relation between α ¯ -harmonic mappings and Euclidean harmonic mappings. As two applications of this representation theorem, we obtain a counterexample of the Radó–Kneser–Choquet theorem for α ¯ -harmonic mappings and show that the Lipschitz continuity of an α ¯ -harmonic mapping with an integer exponent is determined by the Euclidean harmonic mapping with same boundary. [ABSTRACT FROM AUTHOR]