Oscillation and variation for the Hilbert transform

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Strong variational and jump inequalities in harmonic analysis (2008, background): “Variational and jump inequalities in probability, ergodic theory and harmonic analysis have been the subject of many recent articles (see [32], [5], [26], [27], [9], [10], and [28]).”
Oscillation and variation inequalities for convolution powers (2001, methodology): “To handle the variation inequalities for convolution powers operators we will also use some of the techniques we developed in the paper ‘Oscillation and variation for the Hilbert transform’ by Campbell et al in [7].”
Riesz transforms related to Bessel operators (2007, methodology): “5] have obtained a weighted version of the previous result in [6] by proving that the oscillation and variation operators associated with the Hilbert transform are bounded from Lp(v) into itself for every 1 < p < ∞ and v ∈ Ap.”
The ρ-variation as an operator between maximal operators and singular integrals (2009, methodology): “The unweighted version in the case of the Laplacian can be found in [ 6 ] (see Corollaries 2.6 and 2.7).”
Oscillation and variation for singular integrals in higher dimensions (2002, unknown): “The treatment of odd kernels uses the method of rotations, which allows us to directly apply the one-dimensional results from [4].”