Mingquan WEI
,
Dunyan YAN
. SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES[J]. Acta mathematica scientia, Series B, 2018
, 38(2)
: 441
-449
.
DOI: 10.1016/S0252-9602(18)30759-8
[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, Lq)-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 Lp, 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 Lp-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