GENERALIZED HAUSDORFF OPERATORS ON WEIGHTED HERZ SPACES

被引：0

作者：

Kuang Jichang ^{[1
]}

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

来源：

MATEMATICKI VESNIK | 2014年 / 66卷 / 01期

关键词：

Hausdorff operator; weighted Herz space; norm inequality;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce new generalized Hausdorff operators. They include many famous operators as special cases. We obtain necessary and sufficient conditions for these operators to be bounded on the weighted Herz spaces. The corresponding new operator norm inequalities are obtained. They are significant improvements and generalizations of many known results. Several open problems are formulated.

引用

页码：19 / 32

页数：14

共 12 条

[1] [Anonymous], 1967, INEQUALITIES
[2] WEAK-L INFINITY AND BMO
BENNETT, C
DEVORE, RA
SHARPLEY, R
[J]. ANNALS OF MATHEMATICS, 1981, 113 (03) : 601 - 611
[3] Garcia-Cuerva J., 1985, WEIGHTED NORM INEQUA, V116
[4] Hardy G.H., 1933, J LOND MATH SOC, V8, P601
[5] Kuang J.C., 2010, APPL INEQUALITIES, V4th ed.
[6] Multidimensional Hausdorff operators on the real hardy space
Lerner, A. K.
Leflyand, E.
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 83 : 79 - 86
[7] The Hausdorff operator is bounded on the real Hardy space H1(R)
Liflyand, E
Móricz, F
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (05) : 1391 - 1396
[8] Liflyand E., 2006, COMPLEX ANAL POTENTI
[9] Boundedness of the Hausdorff operators in Hp spaces, 0 < p < 1
Liflyand, Elijah
Miyachi, Akihiko
[J]. STUDIA MATHEMATICA, 2009, 194 (03) : 279 - 292
[10] LU SZ, 1995, SCI CHINA SER A, V38, P147

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