Placebo effects on kayak sprint performance in child athletes

Empirical research with adults reveals that performance‐enhancing placebo effects emerge in sports and exercise. However, there is no research on children. Coaches' messages to them could have positive, performance‐improving (placebo) or negative, performance‐impairing (nocebo) effects. This experiment examined the former by ascribing fictive performance‐enhancing properties to an ingredient of the Tic Tac mint to 12 children (aged 12.67 ± SD = 1.83 years), all elite kayakers. Another kayaker was an actor who helped enhance the credibility of the information. The children completed 2‐min kayak ergometer sprints in counterbalanced control and placebo conditions. The measures included heart rate (HR), feeling state, perceived arousal, and expected‐ and perceived‐ performances. Pre‐sprint and maximal HR during the sprint and distance completed in 2 minutes were statistically significantly higher ( p < 0.005) in the placebo than in the control condition without being affected by order effects. While the expected performance in the placebo session was higher ( p = 0.008), perceived performances did not differ statistically between the conditions. This study reveals a sport performance‐related objective, but not subjective, placebo effect in children after a short kayak sprint. The findings have practical implications for performance‐related messages children receive from their coaches and others and show how their altered beliefs can influence their performance

Martingale Hardy Spaces and Some New Weighted Maximal Operators of Fejér Means of Walsh–Fourier Series

In this paper, we introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some “optimal” weights, these new operators indeed are bounded from the martingale Hardy space H_{p}(G) H p ( G ) to the Lebesgue space L_{p}(G) L p ( G ) , for 0<p<1/2 0 < p < 1 / 2 . Moreover, we also prove sharpness of this result. As a consequence, we obtain some new and well-known results