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Journal of Function Spaces and Applications
Volume 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.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Eiichi Nakai, and Gaku Sadasue, “Maximal function on generalized martingale Lebesgue spaces with variable exponent,” Statistics & Probability Letters, 2013. View at Publisher · View at Google Scholar
  • K.-P. Ho, “Atomic decompositions of martingale hardy–morrey spaces,” Acta Mathematica Hungarica, 2016. View at Publisher · View at Google Scholar
  • Eiichi Nakai, and Gaku Sadasue, “Characterizations of boundedness for generalized fractional integrals on martingale morrey spaces,” Mathematical Inequalities and Applications, vol. 20, no. 4, pp. 929–947, 2017. View at Publisher · View at Google Scholar
  • Idha Sihwaningrum, Hendra Gunawan, and Eiichi Nakai, “Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces,” Mathematische Nachrichten, vol. 291, no. 8-9, pp. 1400–1417, 2018. View at Publisher · View at Google Scholar
  • W. Chen, K.-P. Ho, Y. Jiao, and D. Zhou, “Weighted mixed-norm inequality on Doob’s maximal operator and John–Nirenberg inequalities in Banach function spaces,” Acta Mathematica Hungarica, 2018. View at Publisher · View at Google Scholar
  • Lin Yu, Ruhui Wang, and Shoujiang Zhao, “Carleson measures and the generalized Campanato spaces of vector-valued martingales,” Acta Mathematica Scientia, vol. 38, no. 6, pp. 1779–1788, 2018. View at Publisher · View at Google Scholar
  • Kwok-Pun Ho, “Doob's inequality, Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces,” Acta Mathematica Scientia, vol. 38, no. 1, pp. 93–109, 2018. View at Publisher · View at Google Scholar
  • Guangheng Xie, Yong Jiao, and Dachun Yang, “Martingale Musielak-Orlicz Hardy spaces,” Science China Mathematics, 2019. View at Publisher · View at Google Scholar
  • Guangheng Xie, Ferenc Weisz, Dachun Yang, and Yong Jiao, “New martingale inequalities and applications to Fourier analysis,” Nonlinear Analysis, vol. 182, pp. 143–192, 2019. View at Publisher · View at Google Scholar
  • Y. Deng, and L. Li, “Maximal and generalized fractional integral operators in grand Morrey martingale spaces,” Acta Mathematica Hungarica, vol. 158, no. 1, pp. 145–158, 2019. View at Publisher · View at Google Scholar