Integral Representations, Differentiability Properties and Limits at Infinity for Beppo Levi Functions
Integral Representations, Differentiability Properties and Limits at Infinity for Beppo Levi Functions
复制标题
Beppo Levi 函数的积分表示、可微性性质和无穷大极限
DOI：
10.1023/a:1017996900877
复制
发表时间：
1997
影响因子：
1.1
通讯作者：
Y. Mizuta
中科院分区：
文献类型：
--
作者：
Y. Mizuta
本文的第一个目的是给出Rn上Beppo Levi函数的一个积分表示。我们的积分表示是对具有紧支集的无穷可微函数的Soblev积分表示的推广。作为应用，研究了Beppo Levi函数的连续性和可微性。本文的第二个目的是研究Beppo Levi函数在无穷远处的极限的存在性。我们还考虑了关于Bessel容量在无穷远处的精细型极限的存在，从而得到了在无穷远处的径向极限结果。
The first aim in the present paper is to give an integral representation for Beppo Levi functions on Rn. Our integral representation is an extension of Sobolev's integral representation given for infinitely differentiable functions with compact support. As applications, continuity and differentiability properties of Beppo Levi functions are studied.Our second aim in this paper is to study the existence of limits at infinity for Beppo Levi functions. We also consider the existence of fine-type limits at infinity with respect to Bessel capacities, which yields the radial limit result at infinity.