Variation inequalities for the Fejér and Poisson kernels

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Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020, result): “This result relied on a previous result of Lewko and Lewko [52] who in turn invoked a result of Jones and Wang [45].”
Strong q-variation inequalities for analytic semigroups (2011, background): “Many classical sequences of operators and semigroups have been proved to satisfy strong variational bounds, see in particular [9, 17, 18, 19, 26] and references therein.”
Strong variational and jump inequalities in harmonic analysis (2008, background): “The arguments in [37], [29] show that strong q-variational estimates with respect to the martingale sequence in (7) fail whenever q ≤ 2 and hence there are no L bounds for Vq(Af), A = {At} with At in (6), whenever q ≤ 2.”