SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

doi:10.1016/S0252-9602(18)30759-8

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 441-449.doi: 10.1016/S0252-9602(18)30759-8

SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

魏明权¹, 燕敦验²

1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2016-06-07 修回日期:2017-06-23 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Mingquan WEI E-mail:weimingquan11@mails.ucas.ac.cn
作者简介:Dunyan YAN,E-mail:ydunyan@ucas.ac.cn
基金资助:
The work is supported by NSFC (11471309, 11271162, and 11561062), Project of Henan Provincial Department of Education (18A110028), the Nanhu Scholar Program for Young Scholars of XYNU, and Doctoral Scientific Research Startup Fund of Xinyang Normal University (2016).

SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

Mingquan WEI¹, Dunyan YAN²

1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-06-07 Revised:2017-06-23 Online:2018-04-25 Published:2018-04-25
Contact: Mingquan WEI E-mail:weimingquan11@mails.ucas.ac.cn
Supported by:
The work is supported by NSFC (11471309, 11271162, and 11561062), Project of Henan Provincial Department of Education (18A110028), the Nanhu Scholar Program for Young Scholars of XYNU, and Doctoral Scientific Research Startup Fund of Xinyang Normal University (2016).

摘要/Abstract

摘要：

In this article, we obtain the sharp bounds from L^P(Gⁿ) to the space wL^P(Gⁿ) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from L^P(Gⁿ) to the space L^P_I(Gⁿ) are obtained.

关键词: Hardy operators, product spaces, wL^P(Gⁿ), L^P_I(Gⁿ), norm

Abstract:

Key words: Hardy operators, product spaces, wL^P(Gⁿ), L^P_I(Gⁿ), norm

魏明权, 燕敦验. SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES[J]. 数学物理学报(英文版), 2018, 38(2): 441-449.

Mingquan WEI, Dunyan YAN. SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES[J]. Acta mathematica scientia,Series B, 2018, 38(2): 441-449.

参考文献

[1] Hardy G H. Note on a theorem of Hilbert. Math Z, 1920, 6(3/4):314-317
[2] Faris W. Weak lebesgue spaces and quantum mechanincal binding. Duke Math, 1976, 43(2):365-273
[3] Christ M, Grafakos L. Best constants for two nonconvolution inequalities. Proc Amer Math Soc, 1995, 123(6):1687-1693
[4] Pachpatte B G. On multivariale Hardy type inequalities. An Stiint Univ Al I Cuza Iasi, 1992, 38:355-361
[5] Hardy G H, Littlewood J E, Polya G. Inequalities. 2nd ed. Cambridge University Press, 1952
[6] Carton-Lebrun C, Fosset M. Moyennes et quotients de Taylor dans BMO. Bull Soc Roy Sci Liege, 1984, 53:85-87
[7] Benyi A, Oh C T. Best constants for certain multilinear integral operators. J Inequal Appl, 2006, 2006:1-12
[8] Melas A. The best constant for the centered Hardy-Littlewood maximal inequality. Ann Math, 2003, 157:647-688
[9] Brannan D A, Hayman W K. Research problems in complex analysis. Bull London Math Soc, 1989, 21:1-35
[10] Wu D, Wang S M, Yan D Y. (L¹, L^q)-boundedness for Hardy operators with power weight on n-dimensional space. Adv Math (China), 2014, 43:725-732
[11] Benedek A, Panzone R. The space L^p, with mixed norm. Duke Math, 1961, 28:301-324
[12] Benedek A, Calderón P, Panzone R. Convolution operators on Banach space valued functions. Proc Nat Acad Sci, 1962, 48:356-365
[13] Fefferman R, Stein E M. Singular integrals on product spaces. Adv Math, 1982, 45:117-143
[14] Journé J L. Calderón-Zygmund Operators on Product Spaces. Rev Mat Iberoamericana, 1985, 1(3):55-91
[15] Moen K. Linear and multilinear fractional operators:weighted inequalities, sharp bounds, and other properties. University of Kansas, 2009
[16] Fernandez D L. Vector-valued singular integral operators on L^p-spaces with mixed norms and applications. Pacific J Math, 1987, 129(2):257-275
[17] Stefanov A, Torres R H. Calderón-Zygmund operators on mixed Lebesgue spaces and applications to null forms. J London Math Soc, 2004, 70(2):447-462
[18] Rudin W. Real and Complex Analysis. Tata McGraw-Hill Education, 1987
[19] Hardy G H, Littlewood J E, Polya G. Inequalities. Cambridge University Press, 1934
[20] Zhao F Y, Fu Z W, Lu S Z. Endpoint estimates for n-dimensional Hardy operators and their commutators, Sci China Math, 2012, 55(10):1977-1990
[21] Wang S M, Lu S Z, Yan D Y. Explicit constants for Hardy's inequality with power weight on n-dimensional product spaces. Sci China Math, 2012, 55(12):2469-2480
[22] Lu S Z, Yan D Y, Zhao F Y. Sharp bounds for Hardy type operators on higher-dimensional product spaces. J Inequal Appl, 2013, 2013(1):148

SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

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