PM  >> Vol. 7 No. 1 (January 2017)

    Two Weak Endpoint Estimates on Bilinear Hardy Operators

  • 全文下载: PDF(377KB) HTML   XML   PP.43-49   DOI: 10.12677/PM.2017.71007  
  • 下载量: 206  浏览量: 305   科研立项经费支持


张春梅:安徽师范大学数学与计算机科学学院,安徽 芜湖

Hardy算子双线性Hardy算子Lp空间Morrey空间Hardy Operator Multiple Hardy Operator Lp Space Morrey Space



By strict calculation, we mainly give the weak estimate for the boundary of the bilinear Hardy operator on the Morrey space and the weighted Lebesgue space, which is a useful supplement to the existing theory.

张春梅. 关于双线性Hardy算子的两个端点弱型估计[J]. 理论数学, 2017, 7(1): 43-49.


[1] Anderson, K. and Muckenhoupt, B. (1982) Weighted Weak Type Hardy Inequalities with Application to Hilbert Transforms and Maximal Functions. Studia Mathematica, 72, 9-26.
[2] Chen, J.C., Fan, D.S. and Wang, S.L. (2013) Hausdorff Operators on Euclidean Spaces. Applied Mathematics—A Journal of Chinese Universities, 28, 548-564.
[3] Bennet, C., Devore, R.A. and Sharpley, R.C. (1981) Weak and BMO. Annals of Mathematics, 113, 601-611.
[4] Bliss, G.A. (1930) An Integral Inequality. Journal London Mathematical Society, 317, 40-46.
[5] Broadbent, T.A.A. (1928) A Proof of Hardy’s Convergence Theorem. Journal London Mathematical Society, 3, 242- 243.
[6] Levinson, N. (1964) Generalizations of an Inequality of Hardy. Duke Mathematical Journal, 31, 389-394.
[7] Muckenhoupt, B. (1972) Hardy’s Inequality with Weights. Studia Mathematica, 44, 31-38.
[8] Golubov, B.I. (1997) Boundedness of the Hardy and the Hardy-Littlewood Operators in the Spaces ReH1 and BMO. Sbornik: Mathematics, 188, 1041-1054.
[9] Rakotondratsimba, Y. (1998) On the Boundedness of Classical Operators on Weighted Lorentz Spaces. Georgian Mathematical Journal, 5, 177-200.
[10] Calderon, A.P. (1966) Space between and and the Theorem of Marcikiewiez. Studia Mathematica, 26, 273- 299.
[11] Hardy, G.H. (1928) Note on Some Points in the Integral Calculus. Messenger of Mathematics, 57, 12-16.
[12] Martin-Reyes, F. and Ortega, P. (1998) On Weighted Weak Type Inequalities for Modified Hardy Operators. Proceedings of the American Mathematical Society, 126, 1739-1746.
[13] Long, R.L. (1985) Hp Martingale Theory. Peking University Press, Beijing.
[14] Xiao, J. (2001) and BMO Bounds of Weighted Hardy-Littlewood Averages. Journal of Mathematical Analysis and Applications, 262, 660-666.
[15] Hardy, G.H., Littlewood, J.E. and Polya, G. (1934) Inequalities. Cambridge University Press, London and New York.
[16] Edmunds, D., Gurka, P. and Pick, L. (1994) Compactness of Hardy Type Operators in Weighted Banach Function Spaces. Studia Mathematica, 109, 73-90.
[17] Christ, M. and Grafakos, L. (1995) Best Constants for Two Non-Convolution Inequalities. Proceedings of the American Mathematical Society, 123, 1687-1687.
[18] Gao, G., Hu, X. and Zhang, C. (2016) Sharp Weak Estimates for Hardy-Type Operators. Annals of Functional Analysis, 7, 421-433.
[19] Zhao, F.Y., Fu, Z.W. and Lu, S.Z. (2012) Endpoint Estimates for n-Dimensional Hardy Operators and Their Commutators. Science China Mathematics, 55, 1977-1990.
[20] Fu, Z., Grafakos, L., Lu, S.Z., et al. (2012) Sharp Bounds for m-Linear Hardy and Hilbert Operators. Houston Journal of Mathematics, 38, 225-244.
[21] Gao, G. and Zhao, F. (2015) Sharp Weak Bounds for Hausdorff Operators. Analysis Mathematica, 41, 163-173.