分数次积分算子的若干新进展

Recent Progress in the Research on the Fractional Integral Operator

Riesz位势是调和分析中的重要算子 ,具有齐性核或粗糙核的分数次积分 ,是围绕Riesz位势发展起来的一个非常活跃的课题 .近年来 ,关于齐性核 (粗糙核 )分数次积分算子在各种空间上有界性的研究取得了丰富的成果 .

Riesz potential is an important operator in harmonic analysis,and fractional integral with a homogeneous kernel or a coarse kernel is a lively field arising from researches on Riesz potential.Recent years have seen rich achievements about the boundedness of the fractional integral operator with a homogeneous(coarse) kernel in different spaces.Some open problems are mapped out as well as a summary of recent progress in the researches on the fractional integral operator.