Butler, S.; Pavlov, S.; Rosenblatt, J. Large deviations for martingales and derivatives. (English) Zbl 1214.60014 J. Math. Anal. Appl. 366, No. 1, 67-80 (2010). The authors consider large deviations principle for two closely related sequences of linear operators \(T_n\) on \(L_1(\mathbb R):\) one is given by the Lebesgue derivatives and the other one by the dyadic martingale. They prove both positive and negative results concerning the convergence of \[ \sum_{n=1}^{\infty}m \big\{|T_{m_n}f(x)|\geq w_n\big\}, \]where \(m_n\) are positive integer numbers, \(w_n\) are positive real numbers. Reviewer: Anatoliy Swishchuk (Calgary) MSC: 60G42 Martingales with discrete parameter 47B39 Linear difference operators Keywords:martingales; Lebesgue derivatives; large deviations PDFBibTeX XMLCite \textit{S. Butler} et al., J. Math. Anal. Appl. 366, No. 1, 67--80 (2010; Zbl 1214.60014) Full Text: DOI References: [1] Hare, K.; Stokolos, A., On weak type inequalities for rare maximal functions, Colloq. Math., 83, 2, 173-182 (2000) · Zbl 1030.42017 [2] Jones, R.; Kaufman, R.; Rosenblatt, J.; Wierdl, M., Oscillation in ergodic theory, Ergodic Theory Dynam. Systems, 18, 889-935 (1998) · Zbl 0924.28009 [3] Rosenblatt, J.; Wierdl, M., A new maximal inequality and its applications, Ergodic Theory Dynam. Systems, 12, 509-558 (1992) · Zbl 0757.28015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.