中文摘要：

研究两类截断算子从Lp到Lr的有界性问题。需要指出的是,对于某个固定的p,可得到r的一个变化区间,刻画出这个区间与分数阶的关系。此外,还给出算子范数上界的一个估计。

英文摘要：

In this paper,we consider the boundedness of two kinds of the truncated operators from Lpto Lr. For any fixed p we can obtain a variational interval of r,and we characterize the relationship between the interval and the fractional operators. We also give an estimate of the upper bound of the norm of the operator.