The relative mean integral oscillations of a nondecreasing equimeasurable permutation are estimated from above via the same oscillations of the original function. On the basis of this estimate, we establish a lower order-exact estimate for the rate of decrease (vanishing) of the permutation.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 246–260, February, 2019.
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Korenovskyi, A.A. Estimation of the Rate of Decrease (Vanishing) of a Function in Terms of Relative Oscillations. Ukr Math J 71, 278–295 (2019). https://doi.org/10.1007/s11253-019-01644-5
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DOI: https://doi.org/10.1007/s11253-019-01644-5