Abstract :
In this paper we first introduce Ls(μ)-averaging domains which are generalizations of Ls -
averaging domains introduced by S.G. Staples. We characterize Ls(μ)-averaging domains using
the quasihyperbolic metric. As applications, we prove norm inequalities for conjugate A-harmonic
tensors in Ls(μ)-averaging domains which can be considered as generalizations of the Hardy and
Littlewood theorem for conjugate harmonic functions. Finally, we give applications to quasiconformal
and quasiregular mappings.
2003 Elsevier Inc. All rights reserved
