A note on the Hitczenko-Kwapien conjecture about a Rademacher sequence

Shi-Zhen Liu, Ze-Yu Tao, Ze-Chun Hu

Let $({\epsilon }_i)$ be a Rademacher sequence, i.e., a sequence of independent and identically distributed random variables satisfying $P({\epsilon }_i=1)=P({\epsilon }_i=-1)=1/2$. Set $S_n=a_1ε_1+\cdots+a_nε_…