Estimates of M-Harmonic Conjugate Operator

초록

We define the M-harmonic conjugate operator K and prove that for 1 < p < 8, there is a constant C(p) such that integral(S) |Kf|(p)omega d sigma <= C(p) integral(S) |f|(p)omega d sigma for all f is an element of L(p)(omega) if and only if the nonnegative weight. satisfies the Ap- condition. Also, we prove that if there is a constant Cp such that integral(S) |Kf|(p)vd sigma <= C(p) integral(S) |f|(p)wd sigma for all f is an element of L(p)(w), then the pair of weights (v, w) satisfies the A(p)-condition.

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