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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 431692, 11 pages
Boundedness for a Class of Generalized Commutators of Fractional Hardy Operators with a Rough Kernel
1Department of Mathematics, Shangrao Normal University, Shangrao 334001, China
2School of Mathematical Science, Beijing Normal University, Beijing 100875, China
Received 7 July 2013; Accepted 1 October 2013
Academic Editor: Csaba Varga
Copyright © 2013 Xiao Yu and Shanzhen Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. P. Calderón and A. Zygmund, “On singular integrals,” American Journal of Mathematics, vol. 78, pp. 289–309, 1956.
- R. R. Coifman, R. Rochberg, and G. Weiss, “Factorization theorems for Hardy spaces in several variables,” Annals of Mathematics, vol. 103, no. 3, pp. 611–635, 1976.
- J. Cohen, “A sharp estimate for a multilinear singular integral in ,” Indiana University Mathematics Journal, vol. 30, no. 5, pp. 693–702, 1981.
- J. Cohen and J. Gosselin, “A BMO estimate for multilinear singular integrals,” Illinois Journal of Mathematics, vol. 30, no. 3, pp. 445–464, 1986.
- S. Lu and Q. Wu, “CBMO estimates for commutators and multilinear singular integrals,” Mathematische Nachrichten, vol. 276, pp. 75–88, 2004.
- D. Y. Yan, Some problems on multilinear singular integral operators and multilinear oscillatory singular integral operators [Ph.D. thesis], Beijing Normal University, Beijing, China, 2001.
- X. Yu and X. X. Tao, “Boundedness for a class of generalized commutators on λ-central Morrey space,” Acta Mathematica Sinica. English Series, vol. 29, no. 10, pp. 1917–1926, 2013.
- C. Wang and Z. Zhang, “A new proof of Wu's theorem on vortex sheets,” Science China, vol. 55, no. 7, pp. 1449–1462, 2012.
- S. Wu, “Mathematical analysis of vortex sheets,” Communications on Pure and Applied Mathematics, vol. 59, no. 8, pp. 1065–1206, 2006.
- G. H. Hardy, “Note on a theorem of Hilbert,” Mathematische Zeitschrift, vol. 6, no. 3-4, pp. 314–317, 1920.
- Z.-W. Fu, Z.-G. Liu, S.-Z. Lu, and H.-B. Wang, “Characterization for commutators of n-dimensional fractional Hardy operators,” Science in China A, vol. 50, no. 10, pp. 1418–1426, 2007.
- M. Christ and L. Grafakos, “Best constants for two nonconvolution inequalities,” Proceedings of the American Mathematical Society, vol. 123, no. 6, pp. 1687–1693, 1995.
- S. Lu and D. Yang, “The central BMO spaces and Littlewood-Paley operators,” Approximation Theory and its Applications, vol. 11, no. 3, pp. 72–94, 1995.
- Y. Komori, “Notes on singular integrals on some inhomogeneous Herz spaces,” Taiwanese Journal of Mathematics, vol. 8, no. 3, pp. 547–556, 2004.
- S. Z. Lu and F. Y. Zhao, “CBMO estimates for multilinear Hardy operators,” Acta Mathematica Sinica. English Series, vol. 26, no. 7, pp. 1245–1254, 2010.
- G. L. Gao and X. Yu, “Some estimates for the generalized Hardy operators on some function spaces,” Acta Mathematica Sinica. Chinese Series, vol. 55, no. 6, pp. 1101–1110, 2012.
- X. Yu and S. Lu, “Endpoint estimates for generalized commutators of Hardy operators on space,” Journal of Function Spaces and Applications, vol. 2013, Article ID 410305, 11 pages, 2013.
- S. Z. Lu and D. C. Yang, “The decomposition of weighted Herz space and its applications,” Science in China A, vol. 38, no. 2, pp. 147–158, 1995.
- Z. Fu, S. Lu, and F. Zhao, “Commutators of n-dimensional rough Hardy operators,” Science China, vol. 54, no. 1, pp. 95–104, 2011.
- Y. Ding, “A note on multilinear fractional integrals with rough kernel,” Advances in Mathematics, vol. 30, no. 3, pp. 238–246, 2001.
- N. Wiener, “Generalized harmonic analysis,” Acta Mathematica, vol. 55, no. 1, pp. 117–258, 1930.
- A. Beurling, “Construction and analysis of some convolution algebras,” Annales de l'Institut Fourier, vol. 14, pp. 1–32, 1964.
- H. Feichtinger, “An elementary approach to Wiener's third Tauberian theorem on Euclidean n-space,” in Proceedings, Conference at Cortona 1984, vol. 29 of Symposia Mathematica, pp. 267–301, Academic Press, New York, NY, USA, 1987.
- Y. Z. Chen and K.-S. Lau, “Some new classes of Hardy spaces,” Journal of Functional Analysis, vol. 84, no. 2, pp. 255–278, 1989.
- J. García-Cuerva, “Hardy spaces and Beurling algebras,” Journal of the London Mathematical Society, vol. 39, no. 3, pp. 499–513, 1989.
- J. Alvarez, J. Lakey, and M. Guzmán-Partida, “Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures,” Collectanea Mathematica, vol. 51, no. 1, pp. 1–47, 2000.
- Z. W. Fu, Y. Lin, and S. Z. Lu, “λ-central BMO estimates for commutators of singular integral operators with rough kernels,” Acta Mathematica Sinica. English Series, vol. 24, no. 3, pp. 373–386, 2008.
- Z. W. Fu, S. Z. Lu, and W. Yuan, “A weighted variant of Riemann-Liouville fractional integrals on ,” Abstract and Applied Analysis, vol. 2012, Article ID 780132, 18 pages, 2012.