Hardy-Littlewood算子在Lipα(R)(0<α<1)上的有界性

Boundedness of Hardy-Littlewood op erator in space Lipα(R)(0<α<1)

文献[2]中,给出了R上奇偶延拓的Hardy-Littlewood算子的定义,并证明了Hardy-Little-wood算子在函数空间BMO上的有界性.在此基础上进一步研究了该算子在函数空间LiPα(R)(0<α<1)上的性质.通过细致的估计,得到了Hardy-Littlewood算子在LiPα(R)(0<α<1)上也是有界算子的新结果.

Based on the definition of the Hardy -Littlewood operator,which is expan ded to even or odd function in real and the boundedness of the Hardy -Littlewood operator in the space BMO,this paper studies the qualities of operator in the space an d develops the new result of boundedn ess of the Hardy -Littlewood operato r in the space by estimating delicately.