Hardy-Littlewood极大函数双权范数积分不等式的研究
Studies on the integral inequality of two-weight norm of Hardy-Littlewood maximal function
摘要
对于Rn中形如∫J[f*(x)]pU(x)dx≤C∫J|f(x)|pU(x)dx的一类Hardy-Littlewood极大函数f*(x)的积分不等式进行了双权方向的研究,证明了它与权函数Ap条件之间的关系,并进一步推广到了任意测度空间.
The two - weight of the integral inequality of Hardy - Littlewood maximal function f^＊（x） of the form∫J[f^＊（x）]^pU（x）dx≤C∫J｜f（x）｜^pU（x）dx on R^n is researched. The relation between the maximal function andthe conditions of weight function A^p are testified, and then the relation is extended to the any measure spaces.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2007年第4期543-547,560,共6页
Journal of Natural Science of Heilongjiang University
参考文献7
-
1Hardy G H,Linlewood J E.A maximal theorem with function-theoretic application[J].Acta Math,1930,54:81-116. 被引量：1
-
2Stein E M.On certain operators on Lp spaces[D].Chicago:University of Chicago,1955. 被引量：1
-
3Fefferma C,Stein E M.Some Maximal inequalities[J].Amer J Math,1971,93:107-115. 被引量：1
-
4Muckonhonpt B B.Weighted norm inequalities for the hardy maximal function Amer[J].Mathematical Society,1972,165:207-226. 被引量：1
-
5Ding S,Weighted hardy-littlewood inequality for A-harmonic temors[J].Proc Amer Math Soc,1997,125:1727-1735. 被引量：1
-
6Cruz-Uribe D,SFO,Peter C.Two-weight weak-type norm inequalites for fractional integrals,Calderon-Zygmund operators and commutators[J].Indiana University Mathematics Journal,2000,49(2):697-721. 被引量：1
-
7Zymund A.Trigonometric series(Ⅰ,Ⅱ)[M].2nd ed.New York:cambridge Univ Press,1959. 被引量：1
