- 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 829218, 9 pages
Estimates of Some Operators on One-Sided Weighted Morrey Spaces
Department of Mathematics, Linyi University, Linyi 276005, China
Received 13 August 2013; Revised 30 September 2013; Accepted 3 October 2013
Academic Editor: Bashir Ahmad
Copyright © 2013 Shaoguang Shi and Zunwei Fu. 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.
- F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weights for one-sided operators,” in Recent Development in Real and Harmonic Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 2009.
- P. Butzer and U. Westphal, “Introduction to fractional calculus,” in Fractional Calculus, Applications in Physics, H. Hilfer, Ed., pp. 1–85, World Scientific, Singapore, 2000.
- 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.
- E. Sawyer, “Weighted inequalities for the one-sided Hardy-Littlewood maximal functions,” Transactions of the American Mathematical Society, vol. 297, no. 1, pp. 53–61, 1986.
- H. Aimar, L. Forzani, and F. J. Martín-Reyes, “On weighted inequalities for singular integrals,” Proceedings of the American Mathematical Society, vol. 125, no. 7, pp. 2057–2064, 1997.
- K. F. Andersen and E. T. Sawyer, “Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators,” Transactions of the American Mathematical Society, vol. 308, no. 2, pp. 547–558, 1988.
- Z. Fu, S. Lu, S. Sato, and S. Shi, “On weighted weak type norm inequalities for one-sided oscillatory singular integrals,” Studia Mathematica, vol. 207, no. 2, pp. 137–151, 2011.
- F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weighted inequalities for one-sided maximal functions,” Transactions of the American Mathematical Society, vol. 319, no. 2, pp. 517–534, 1990.
- F. J. Martín-Reyes and A. de la Torre, “One-sided BMO spaces,” Journal of the London Mathematical Society, vol. 49, no. 3, pp. 529–542, 1994.
- F. J. Martín-Reyes and A. de la Torre, “Two weight norm inequalities for fractional one-sided maximal operators,” Proceedings of the American Mathematical Society, vol. 117, no. 2, pp. 483–489, 1993.
- H. Aimar and R. Crescimbeni, “On one-sided BMO and Lipschitz functions,” Annali della Scuola Normale Superiore di Pisa Serie IV, vol. 27, no. 3-4, pp. 437–456, 1998.
- Z. W. Fu and S. Z. Lu, “One-sided Triebel-Lizorkin space and its applications,” Scientia Sinica Mathematica, vol. 41, pp. 43–52, 2011.
- S. Ombrosi and L. de Rosa, “Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces,” Publicacions Matemàtiques, vol. 47, no. 1, pp. 71–102, 2003.
- L. de Rosa and C. Segovia, “Equivalence of norms in one-sided spaces,” Collectanea Mathematica, vol. 53, no. 1, pp. 1–20, 2002.
- P. G. Lemarié-Rieusset, “The Navier-Stokes equations in the critical Morrey-Campanato space,” Revista Matemática Iberoamericana, vol. 23, no. 3, pp. 897–930, 2007.
- G. Lu, “Embedding theorems on Campanato-Morrey spaces for vector fields and applications,” Comptes Rendus de l'Académie des Sciences. Série I., vol. 320, no. 4, pp. 429–434, 1995.
- G. Lu, “Embedding theorems on Campanato-Morrey spaces for vector fields on Hörmander type,” Approximation Theory and Its Applications, vol. 14, no. 1, pp. 69–80, 1998.
- H. Triebel, Theory of Function Spaces. II, vol. 84 of Monographs in Mathematics, Birkhäuser, Basel, Switzerland, 1992.
- X. T. Duong, J. Xiao, and L. Yan, “Old and new Morrey spaces with heat kernel bounds,” The Journal of Fourier Analysis and Applications, vol. 13, no. 1, pp. 87–111, 2007.
- H. Lin, E. Nakai, and D. Yang, “Boundedness of Lusin-area and functions on localized Morrey-Campanato spaces over doubling metric measure spaces,” Journal of Function Spaces and Applications, vol. 9, no. 3, pp. 245–282, 2011.
- D. Yang, D. Yang, and Y. Zhou, “Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrödinger operators,” Nagoya Mathematical Journal, vol. 198, pp. 77–119, 2010.
- C. B. Morrey Jr., “On the solutions of quasi-linear elliptic partial differential equations,” Transactions of the American Mathematical Society, vol. 43, no. 1, pp. 126–166, 1938.
- D. Fan, Y. Pan, and D. Yang, “A weighted norm inequality for rough singular integrals,” The Tohoku Mathematical Journal, vol. 51, no. 2, pp. 141–161, 1999.
- D. Fan, S. Lu, and D. Yang, “Boundedness of operators in Morrey spaces on homogeneous spaces and its applications,” Acta Mathematica Sinica, vol. 14, pp. 625–634, 1998.
- W. Yuan, W. Sickel, and D. Yang, Morrey and Campanato meet Besov, Lizorkin and Triebel, vol. 2005 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010.
- R. R. Coifman and C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals,” Polska Akademia Nauk, vol. 51, pp. 241–250, 1974.
- P. Guan and E. Sawyer, “Regularity estimates for the oblique derivative problem,” Annals of Mathematics, vol. 137, no. 1, pp. 1–70, 1993.
- L. De Rosa and C. Segovia, “Dual spaces for one-sided weighted Hardy spaces,” Revista de la Unión Matemática Argentina, vol. 40, no. 3-4, pp. 49–71, 1997.
- M. S. Riveros and A. de la Torre, “On the best ranges for and ,” Czechoslovak Mathematical Journal, vol. 51, no. 2, pp. 285–301, 2001.
- X. W. Li and D. C. Yang, “Boundedness of some sublinear operators on Herz spaces,” Illinois Journal of Mathematics, vol. 40, no. 3, pp. 484–501, 1996.