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

초록

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 A(p)-condition, and ud sigma, vd sigma are doubling measures, where d sigma is the rotation-invariant 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 A(p)-condition, and vd sigma does a certain regular condition.

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