Comparison of moments for tangent sequences of random variables (Q1094732)

It is shown that for all tangent sequences \((d_ n)\) and \((e_ n)\) of nonnegative or conditionally symmetric random variables and for every function \(\Phi\) satisfying the growth condition \(\Phi\) (2x)\(\leq \alpha \Phi (x)\) the following inequality holds: \[ E \Phi (\sup _{n}| \sum ^{n}_{k=1}d_ k|)\leq cE \Phi (\sup _{n}| \sum ^{n}_{k=1}e_ k|). \] This generalizes results of J. Zinn and proves a conjecture of S. Kwapień and W. A. Woyczyński.