局部紧的Vilenkin群上的广义分数次积分算子  

The Generalized Fractional Integral on the Locally Compact Vilenkin Group

作　　者：汤灿琴[1] 李庆国[1] 马柏林[1] 

机构地区：[1]湖南大学数学与计量学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2005年第5期120-123,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(10371004)

摘　　要：G表示局部紧的Vilenkin群.作者对Vilenkin群G上的标准分数次积分算子进行柘广,首次引入了在G上的θ型分数次积分算子,并对它进行了详细的研究.利用Hardy空间和Herz型Hardy空间的原子和分子分解特征,文中首先给出了此类算子从Hardy空间到Lebesgue空间上的有界性,而且,在满足一定的消失矩时,它又是Hardy空间上的有界算子.更进一步地,文章还讨论了这类算子在Herz型Hardy空间上的有界性.Let G be a locally compact Vilenkin group, and we extended the case of standard fractional integral operators on the Vilenkin group G. A θ-type of fractional integral operators was introduced, and its properties were given. We proved that this kind of operators were bounded from Hardy space to Lebesgue space, and they were bounded operators on the Hardy space if they satisfied some special conditions. Furthermore, the boundedness on Herz-type Hardy space were also discussed.

关 键 词：分数次积分算子 HARDY空间 HERZ型HARDY空间 VILENKIN群 

分 类 号：O177.5[理学—数学]