2017 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We study the classes (Equation presented) and (Equation presented) A highlight of this paper is the asymptotically sharp inequality (Equation presented) where n converges to 0 rapidly as n tends to 00. The inequality (Equation presented) is also established. Our results improve an old result due to Halsz and a recent result due to Ks. We prove several other related order-sharp results in this paper. Bibliography: 33 titles.
