On hypersingular integrals and Lebesgue spaces of differentiable functions. II
On hypersingular integrals and Lebesgue spaces of differentiable functions. II
复制标题
DOI：
10.1090/s0002-9947-1968-0232249-1
复制
发表时间：
1968-03
影响因子：
1.3
通讯作者：
R. Wheeden
中科院分区：
文献类型：
--
作者：
R. Wheeden
J ' f称为/的a阶贝塞尔势，众所周知，J ' f=f* Ga，其中g = 0, J ' n Ga(x) dx = \。我们用L\所有Lp函数/=7°#=*Ga表示其中j>eLp，并写为= j ~af′|/||”，a= ||<¿[|p。为了讨论Lp空间的性质，我们建议读者参考[1]和[2]。本文的目的是推广e.m. Stein在[7]中提出的定理。
J"f is called the Bessel potential of order a of/, and it is well known that J"f=f* Ga where Gœ = 0 and J£n Ga(x) dx = \.We denote by L\ all Lp functions/=7°#=*Ga where j>eLp, and write =J~af ¡|/||„,a= ||<¿[|p. For a discussion of the properties of the Lp spaces, we refer the reader to [1] and [2]. The purpose of this paper is to generalize the following theorem of E. M. Stein stated in [7].