Copyright © 2010 Peilin Shi and Shusen Ding. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove the new versions of the weighted Hardy-Littlewood inequality and Caccioppoli-type inequality for -harmonic tensors. We also explore applications of our results to -quasiregular mappings and -harmonic functions in .