%0 Journal Article
%T 具有可变核的多线性积分算子在变指数Lebesgue空间的有界性<br>The Boundedness of Multilinear Fractional Integral Operators with Variable Kernel on Variable Exponent Lebesgue Spaces
%A 万秋阅
%A 吴慧伶
%A 兰家诚
%J Pure Mathematics
%P 72-80
%@ 2160-7605
%D 2016
%I Hans Publishing
%R 10.12677/PM.2016.61011
%X <div style=\"text-align:justify;\">
	<span style=\"line-height:1.5;\">本文研究了具有可变核的多线性分数次积分算子和相对应的极大算子的有界性，通过多线性分数次积分与对应的分数次积分的联系，将多线性转化为较为简单的分数次积分，从而得到算子<img src=\"Edit_095d73c2-3727-48d6-8477-716552307c6e.png\" width=\"50\" height=\"26\" alt=\"\" /> 和<img src=\"Edit_1bbff423-c218-470e-878d-3383a13f4855.png\" width=\"50\" height=\"26\" alt=\"\" /> 在<img src=\"Edit_088d4057-8a97-4a13-bbfb-bb2880431296.png\" width=\"50\" height=\"26\" alt=\"\" /> 上是有界的。<br />
In this paper, the authors study the boundedness of a class of multilinear fractional integral and the maximal operators with variable kernel. Under some assumptions, it is obtained that these operators <img src=\"Edit_a1323bbe-a8b6-428e-a5fa-d5cb9902a3af.png\" width=\"50\" height=\"26\" alt=\"\" /> and <img src=\"Edit_c30eda57-51a1-4175-88fa-173ea70bd2f5.png\" width=\"50\" height=\"26\" alt=\"\" /> are both bounded from<img src=\"Edit_6f7293da-3edf-4e7c-8965-be84845b4fbd.png\" width=\"50\" height=\"26\" alt=\"\" /> to <img src=\"Edit_113085b9-1586-49a3-ba55-ab6c3e0015ea.png\" width=\"50\" height=\"26\" alt=\"\" /> by using the connection between multilinear and fractional integral operators and converting multilinear into simple fractional integral.</span><span style=\"line-height:1.5;\"></span> 
</div>
%K 多线性分数次积分，可变核，变指数Lebesgue空间<br>Multilinear Fractional Integral
%K Variable Kernel
%K Variable Exponent Lebesgue Spaces
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=16858