Abstract
In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps Lp(ℝ,w(x)dx) into itself when w is a weight in the Ap class for 1 < p < ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.
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