- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 196459, 8 pages
Morrey Spaces for Nonhomogeneous Metric Measure Spaces
Department of Mathematics, Xinjiang University, Urumqi 830046, China
Received 6 May 2013; Accepted 14 August 2013
Academic Editor: Vakhtang M. Kokilashvili
Copyright © 2013 Cao Yonghui and Zhou Jiang. 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.
- J. García-Cuerva and A. E. Gatto, “Boundedness properties of fractional integral operators associated to non-doubling measures,” Studia Mathematica, vol. 162, no. 3, pp. 245–261, 2004.
- G. Hu, Y. Meng, and D. Yang, “Multilinear commutators for fractional integrals in non-homogeneous spaces,” Publicacions Matemàtiques, vol. 48, no. 2, pp. 335–367, 2004.
- X. Tolsa, “BMO, , and Calderón-Zygmund operators for non doubling measures,” Mathematische Annalen, vol. 319, no. 1, pp. 89–149, 2001.
- X. Tolsa, “Littlewood-Paley theory and the T(1) theorem with non-doubling measures,” Advances in Mathematics, vol. 164, no. 1, pp. 57–116, 2001.
- X. Tolsa, “The space for nondoubling measures in terms of a grand maximal operator,” Transactions of the American Mathematical Society, vol. 355, no. 1, pp. 315–348, 2003.
- X. Tolsa, “Painlevé's problem and the semiadditivity of analytic capacity,” Acta Mathematica, vol. 190, no. 1, pp. 105–149, 2003.
- X. Tolsa, “The semiadditivity of continuous analytic capacity and the inner boundary conjecture,” American Journal of Mathematics, vol. 126, no. 3, pp. 523–567, 2004.
- W. Chen, Y. Meng, and D. Yang, “Calderón-Zygmund operators on Hardy spaces without the doubling condition,” Proceedings of the American Mathematical Society, vol. 133, no. 9, pp. 2671–2680, 2005.
- W. Chen and E. Sawyer, “A note on commutators of fractional integrals with (u) functions,” Illinois Journal of Mathematics, vol. 46, no. 4, pp. 1287–1298, 2002.
- T. Hytönen, “A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa,” Publicacions Matemàtiques, vol. 54, no. 2, pp. 485–504, 2010.
- T. A. Bui and X. T. Duong, “Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces,” Journal of Geometric Analysis, vol. 23, no. 2, pp. 895–932, 2013.
- T. Hytönen, S. Liu, D. Yang, and D. Yang, “Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces,” Canadian Journal of Mathematics, vol. 64, no. 4, pp. 892–923, 2012.
- J. Zhou and B. L. Ma, “Marcinkiewicz commutators with Lipschitz functions in non-homogeneous spaces,” Canadian Mathematical Bulletin, vol. 55, no. 3, pp. 646–662, 2012.
- T. Hytönen, D. Yang, and D. Yang, “The Hardy space on non-homogeneous metric spaces,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 153, no. 1, pp. 9–31, 2012.
- H. Lin, E. Nakai, and D. Yang, “Boundedness of Lusin-area and functions on localized BMO spaces over doubling metric measure spaces,” Bulletin des Sciences Mathématiques, vol. 135, no. 1, pp. 59–88, 2011.
- H. Lin and D. Yang, “An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces,” Banach Journal of Mathematical Analysis, vol. 6, no. 2, pp. 168–179, 2012.
- S. Liu, D. Yang, and D. Yang, “Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces: equivalent characterizations,” Journal of Mathematical Analysis and Applications, vol. 386, no. 1, pp. 258–272, 2012.
- Y. Sawano and H. Tanaka, “Morrey spaces for non-doubling measures,” Acta Mathematica Sinica, vol. 21, no. 6, pp. 1535–1544, 2005.
- Y. Sawano, “-valued extension of the fractional maximal operators for non-doubling measures via potential operators,” International Journal of Pure and Applied Mathematics, vol. 26, no. 4, pp. 505–523, 2006.
- Y. Sawano and H. Tanaka, “Equivalent norms for the Morrey spaces with non-doubling measures,” Far East Journal of Mathematical Sciences, vol. 22, no. 3, pp. 387–404, 2006.
- F. Chiarenza and M. Frasca, “Morrey spaces and Hardy-Littlewood maximal function,” Rendiconti di Matematica e delle sue Applicazioni, vol. 7, no. 3-4, pp. 273–279, 1987.
- X. Fu, D. Yang, and W. Yuan, “Generalized fractional integrals and their commutators over non-homogeneous spaces,” 2012.
- H. Lin and D. Yang, “Equivalent Boundedness of Marcinkiewicz integrals on nonhomogeneous metric measure spaces,” 2012.
- V. S. Guliyev and Y. Sawano, “Linear and sublinear operators on Generalized Morrey spaces with non-doubling measures,” Publicationes Mathematicae Debrecen, vol. 83, no. 3, pp. 1–17, 2013.
- J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, New York, NY, USA, 2001.
- G. Di Fazio and M. A. Ragusa, “Commutators and Morrey spaces,” Unione Matematica Italiana. Bollettino A, vol. 5, no. 3, pp. 323–332, 1991.
- J. Peetre, “On the theory of spaces,” Journal of Functional Analysis, vol. 4, pp. 71–87, 1969.
- V. Kokilashvili and A. Meskhi, “Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure,” Complex Variables and Elliptic Equations, vol. 55, no. 8–10, pp. 923–936, 2010.
- L. I. Hedberg, “On certain convolution inequalities,” Proceedings of the American Mathematical Society, vol. 36, pp. 505–510, 1972.
- D. E. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and Compact Integral Operators, chapter 6, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.
- I. Sihwaninggrum and Y. Sawano, “Weak and strong type estimates for fractional integral opertors on Morrey spaces in metric measure spaces,” Eurasian Mathematical Journal, vol. 4, no. 1, pp. 76–81, 2013.
- A. Eridani, V. Kokilashvili, and A. Meskhi, “Morrey spaces and fractional integral operators,” Expositiones Mathematicae, vol. 27, no. 3, pp. 227–239, 2009.
- D. R. Adams, “A note on Riesz potentials,” Duke Mathematical Journal, vol. 42, no. 4, pp. 765–778, 1975.