Department of Mathematics, Sogang University, 1 Sinsu-dong, Mapo-gu, Seoul 121-742, South Korea
Copyright © 2010 Jaesung Lee and Kyung Soo Rim. 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 define the -harmonic conjugate operator and prove that for , there is a constant such that for all if and only if the nonnegative weight satisfies the -condition. Also, we prove that if there is a constant such that for all , then the pair of weights satisfies the -condition.