Hardy-Littlewood极大函数在加权Orlicz—Morrey空间上的有界性
The Boundedness of the Hardy Littlewood Maximal Function on the Weighted Orlicz-Morrey Spaces
摘要
本文得到了极大函数Mω(|f|^p)^1/p;和M(f)在加权Orlicz-Morrey空间上的有界性,同时也给出了极大函数Mω(|f|^p)^1/p在其上有界的必要条件.
We obtain the boundedness of the maximal operator Mω(|f|^p)^1/p, and M(f) on the weighted Orlicz Morrey spaces. On the other hand, we get a necessary condition for the boundedness of the maximal operator Mω(|f|^p)^1/p.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2011年第5期721-730,共10页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(10931001
10871173)
参考文献11
-
1Cianchi A., Strong and weak type inequalities for some classical operators in Orlicz spaces, J. London. Math. Soc., 1999, 60(2): 187-202.
-
2Kita H., On maximal functions in Orlicz spaces, Ibid., 1996, 124:3019 3025.
-
3Kita H., On Hardy-Littlewood maximal functions in Orlicz spaces, Math. Nachr., 1997, 183:135 155.
-
4Morrey C. B., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc.,1938, 43: 126-166.
-
5Chiarenza F., Frasca M., Morrey spaces and Hardy-Littlewood maximal function, Rend. Math. Appl., 1987, 7(7): 273-279.
-
6Nakai E., Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr., 1994. 166:95-103.
-
7Peetre J., On the theory of Lp,λ spaces, J. Funct. Anal., 1969, 4:71 87.
-
8Nakai E., Orlicz Morrey spaces and the Hardy-Littlewood maximal function, Studia. Math., 2008, 183(3): 193-221.
-
9Bloom S., Kerman R., Weighted Orlicz space integral inequalities for the Hardy Littlewood maximal operator, Studia. Math., 1994, 110(2): 149-167.
-
10Komori Y., Shirai S., Weighted Morrey spaces and a singular integral operator, Math. Nachr., 2009, 282(2): 219-231.