自由无限可分分布与Lévy测度的可积性
Integrability of Freely Infinitely Divisible Distributions and Lévy Measures
AI总结：
该研究证明了自由无限可分分布的可积性等价于其自由Lévy测度大跳跃部分的可积性，还得到了相关尾比较、一致可积性及分数自由卷积幂的可积性结果。
AI中文摘要：
在递增函数g的增长条件下，我们证明：关于g的自由无限可分分布的可积性，等价于其自由Lévy测度的大跳跃部分的可积性。对每个递增的自由次乘性函数g，该分布的可积性都意味着其自由Lévy测度的大跳跃部分的可积性。我们还得到了自由无限可分分布与其自由Lévy测度之间的双侧尾比较、自由卷积半群上的一致可积性，以及分数自由卷积幂的可积性结果与尾估计。
英文摘要：
Under a growth condition on an increasing function $g$, we prove that integrability of a freely infinitely divisible distribution with respect to $g$ is equivalent to that of the large-jump part of its free Lévy measure. For every increasing freely submultiplicative function $g$, integrability of the distribution implies integrability of the large-jump part of its free Lévy measure. We also obtain two-sided tail comparisons between freely infinitely divisible distributions and their free Lévy measures, uniform integrability along free convolution semigroups, and integrability results and tail estimates for fractional free convolution powers.
