# Norm inequalities for the conjugate operator in two-weighted Lebesgue spaces

• Published 2012

#### Abstract

* Correspondence: ksrim@sogang. ac.kr Department of Mathematics, Sogang University, Seoul 121-742, Korea Abstract In this article, first, we prove that weighted-norm inequalities for the M-harmonic conjugate operator on the unit sphere whenever the pair (u, v) of weights satisfies the Ap-condition, and uds, vds are doubling measures, where ds is the rotationinvariant positive Borel measure on the unit sphere with total measure 1. Then, we drive cross-weighted norm inequalities between the Hardy-Littlewood maximal function and the sharp maximal function whenever (u, v) satisfies the Ap-condition, and vds does a certain regular condition. 2000 MSC: primary 32A70; secondary 47G10.

### Cite this paper

@inproceedings{Rim2012NormIF, title={Norm inequalities for the conjugate operator in two-weighted Lebesgue spaces}, author={Kyung Soo Rim and Jaesung S. Lee}, year={2012} }