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Weighted maximal functions and derivatives of invariant Poisson integrals of potentials

Weighted maximal functions and derivatives of invariant Poisson integrals of potentials

In this paper we prove LP estimates for weighted maximal functions of invariant Poisson integrals of potentials. From this it follows that the exceptional sets of the Poisson integrals of potentials are sets of zero Hausdorff capacity. Let S denote the boundary of Bn , the unit ball in Cn …