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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 281562, 10 pages
Weighted Endpoint Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operators
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Received 14 May 2013; Accepted 1 October 2013
Academic Editor: Baoxiang Wang
Copyright © 2013 Yu Liu et al. 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.
- 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.
- Z. Guo, P. Li, and L. Peng, “ boundedness of commutators of Riesz transforms associated to Schrödinger operator,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 421–432, 2008.
- P. Li and L. Peng, “Endpoint estimates for commutators of Riesz transforms associated with Schrödinger operators,” Bulletin of the Australian Mathematical Society, vol. 82, no. 3, pp. 367–389, 2010.
- B. Bongioanni, E. Harboure, and O. Salinas, “Commutators of Riesz transforms related to Schrödinger operators,” The Journal of Fourier Analysis and Applications, vol. 17, no. 1, pp. 115–134, 2011.
- B. Bongioanni, E. Harboure, and O. Salinas, “Weighted inequalities for commutators of Schrödinger-Riesz transforms,” Journal of Mathematical Analysis and Applications, vol. 392, no. 1, pp. 6–22, 2012.
- Y. Liu, “Commutators of BMO functions and degenerate Schrödinger operators with certain nonnegative potentials,” Monatshefte für Mathematik, vol. 165, no. 1, pp. 41–56, 2012.
- Y. Liu, J. Z. Huang, and J. F. Dong, “Commutators of higher order Riesz transform associated with Schrödinger operators,” Journal of Function Spaces and Applications, vol. 2013, Article ID 842375, 15 pages, 2013.
- Y. Liu, J. Z. Huang, and J. F. Dong, “Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators,” Science China Mathematics, vol. 56, no. 9, pp. 1895–1913, 2013.
- Z. W. Shen, “ estimates for Schrödinger operators with certain potentials,” Annales de l'Institut Fourier, vol. 45, no. 2, pp. 513–546, 1995.
- J. Dziubański and J. Zienkiewicz, “Hardy space associated to Schrödinger operator with potential satisfying reverse Hölder inequality,” Revista Matemática Iberoamericana, vol. 15, no. 2, pp. 279–296, 1999.
- H. Liu, L. Tang, and H. Zhu, “Weighted Hardy spaces and BMO spaces associated with Schrödinger operators,” Mathematische Nachrichten, vol. 285, no. 17-18, pp. 2173–2207, 2012.
- D. Yang and Y. Zhou, “Localized Hardy spaces related to admissible functions on RD-spaces and applications to Schrödinger operators,” Transactions of the American Mathematical Society, vol. 363, no. 3, pp. 1197–1239, 2011.
- E. M. Stein, Real-Variable Methods, Orthogonality, and Oscillatory Integrals, vol. 43 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, 1993.
- J. Duoandikoetxea, Fourier Analysis, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2001.
- C. C. Lin, H. P. Liu, and Y. Liu, “Hardy spaces associated with Schrödinger operators on the Heisenberg group,” http://arxiv.org/abs/1106.4960.
- J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, vol. 116 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 1985.