Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 690258, 14 pages
http://dx.doi.org/10.1155/2013/690258
Research Article

Martingale Morrey-Hardy and Campanato-Hardy Spaces

1Department of Mathematics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
2Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
3Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Osawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan

Received 10 June 2013; Accepted 17 August 2013

Academic Editor: Natasha Samko

Copyright © 2013 Eiichi Nakai 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.

Linked References

  1. J. Peetre, “On the theory of p,λ spaces,” Journal of Functional Analysis, vol. 4, no. 1, pp. 71–87, 1969. View at Google Scholar · View at Scopus
  2. W. Yuan, W. Sickel, and D. Yang, Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. F. Weisz, “Martingale Hardy spaces for 0<P1,” Probability Theory and Related Fields, vol. 84, no. 3, pp. 361–376, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  4. T. Miyamoto, E. Nakai, and G. Sadasue, “Martingale Orlicz-Hardy spaces,” Mathematische Nachrichten, vol. 285, no. 5-6, pp. 670–686, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  5. E. Nakai and G. Sadasue, “Martingale Morrey-Campanato spaces and fractional integrals,” Journal of Function Spaces and Applications, vol. 2012, Article ID 673929, 29 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J.-A. Chao and H. Ombe, “Commutators on dyadic martingales,” Proceedings of the Japan Academy, vol. 61, no. 2, pp. 35–38, 1985. View at Google Scholar · View at MathSciNet
  7. C. Watari, “Multipliers for Walsh-Fourier series,” The Tohoku Mathematical Journal, vol. 16, pp. 239–251, 1964. View at Google Scholar · View at MathSciNet
  8. G. H. Hardy and J. E. Littlewood, “Some properties of fractional integrals. I,” Mathematische Zeitschrift, vol. 27, no. 1, pp. 565–606, 1928. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. H. Hardy and J. E. Littlewood, “Some properties of fractional integrals. II,” Mathematische Zeitschrift, vol. 34, no. 1, pp. 403–439, 1932. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. L. Sobolev, “On a theorem in functional analysis,” Matematicheskii Sbornik, vol. 4, pp. 471–497, 1938. View at Google Scholar
  11. E. M. Stein and G. Weiss, “On the theory of harmonic functions of several variables. I. The theory of Hp-spaces,” Acta Mathematica, vol. 103, pp. 25–62, 1960. View at Google Scholar · View at MathSciNet
  12. M. H. Taibleson and G. Weiss, “The molecular characterization of certain Hardy spaces,” in Representation theorems for Hardy spaces, vol. 77 of Astérisque, pp. 67–149, Soc. Math. France, Paris, 1980. View at Google Scholar · View at MathSciNet
  13. S. G. Krantz, “Fractional integration on Hardy spaces,” Studia Mathematica, vol. 73, no. 2, pp. 87–94, 1982. View at Google Scholar · View at MathSciNet
  14. E. Nakai, “Recent topics of fractional integrals,” Sugaku Expositions, vol. 20, no. 2, pp. 215–235, 2007. View at Google Scholar · View at MathSciNet
  15. D. R. Adams, “A note on Riesz potentials,” Duke Mathematical Journal, vol. 42, no. 4, pp. 765–778, 1975. View at Google Scholar · View at MathSciNet
  16. 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. View at Google Scholar · View at MathSciNet
  17. H. Tanaka and Y. Terasawa, “Positive operators and maximal operators in a filtered measure space,” Journal of Functional Analysis, vol. 264, no. 4, pp. 920–946, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, The Netherlands, 1975. View at MathSciNet
  19. F. Weisz, Martingale Hardy Spaces and Their Applications in Fourier Analysis, vol. 1568 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1994. View at MathSciNet
  20. D. L. Burkholder, “Martingale transforms,” Annals of Mathematical Statistics, vol. 37, pp. 1494–1504, 1966. View at Google Scholar · View at MathSciNet
  21. D. L. Burkholder, “Sharp inequalities for martingales and stochastic integrals, Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987),” Astérisque, no. 157-158, pp. 75–94, 1988. View at Google Scholar · View at MathSciNet
  22. D. L. Burkholder, “Explorations in martingale theory and its applications,” in École d’Été de Probabilités de Saint-Flour XIX 1989, vol. 1464 of Lecture Notes in Mathematics, pp. 1–66, Springer, Berlin, Germany, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. L. Long, Martingale Spaces and Inequalities, Peking University Press, Beijing, China, 1993. View at MathSciNet
  24. M. Kikuchi, “Characterization of Banach function spaces that preserve the Burkholder square-function inequality,” Illinois Journal of Mathematics, vol. 47, no. 3, pp. 867–882, 2003. View at Google Scholar · View at MathSciNet
  25. F. Weisz, “Interpolation between martingale Hardy and BMO spaces, the real method,” Bulletin des Sciences Mathématiques, vol. 116, no. 2, pp. 145–158, 1992. View at Google Scholar · View at MathSciNet
  26. E. Nakai, “On generalized fractional integrals,” Taiwanese Journal of Mathematics, vol. 5, no. 3, pp. 587–602, 2001. View at Google Scholar · View at MathSciNet
  27. H. Gunawan, “A note on the generalized fractional integral operators,” Journal of the Indonesian Mathematical Society, vol. 9, no. 1, pp. 39–43, 2003. View at Google Scholar · View at MathSciNet
  28. G. Sadasue, “Fractional integrals on martingale Hardy spaces for 0<P1,” Memoirs of Osaka Kyoiku University, vol. 60, no. 1, pp. 1–7, 2011. View at Google Scholar · View at MathSciNet
  29. Y. Sawano and H. Tanaka, “Sharp maximal inequalities and commutators on Morrey spaces with non-doubling measures,” Taiwanese Journal of Mathematics, vol. 11, no. 4, pp. 1091–1112, 2007. View at Google Scholar · View at MathSciNet
  30. H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, Switzerland, 1983. View at Publisher · View at Google Scholar · View at MathSciNet