Hölder Continuity of Generalized Harmonic Functions in the Unit Disc

In this paper, we study Hölder continuity of (p, q)-harmonic functions defined on the unit disc D as the Poisson type integral u= K_p,q[f] of a β-Hölder function f∈ Λ _β(T) on the unit circle T. Mainly, we consider three cases, when p+ q> β- 1 , we show that u∈ Λ _β(D) , whereas in the case p+ q< β- 1 , we prove that u∈ Λ _p+q+1(D) , and when p+ q= β- 1 , we show that u∈ ⋂ _<α<βΛ _α(D). Finally, we show the stability of the exponents of f and u in their corresponding Lipschitz spaces under the condition u is K-quasiconformal.