Two-weighted Integral Inequalities For Conjugate A-Harmonic Tensors And A-Harmonic Functions

Weighted integral inequalities are generalizations of some important inequalities. They have important applications in geometric function theory and nonlinear analysis. Many weighted intergral inequalities are obtained only when 0 <α<1, while less is known forα=1. In this paper, we first introduce a kind of weight-- A_r^λ₃(λ₁,λ₂,Ω), then, we derive local two-weighted Hardy-Littlewood inequality for conjugate A-harmonic tensors whenα=1 and local two-weighted Poincaréinequality for A- harmonic functions whenα=1 and 0 <α<1. Finally, we give some applications of the above results to quasiregular mappings.