Tohoku Mathematical Journal

Some new properties concerning BLO martingales

Eiichi Nakai and Gaku Sadasue

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Some new properties concerning BLO martingales are given. The BMO-BLO boundedness of martingale maximal functions and Bennett type characterization of BLO martingales are shown. Also, a non-negative BMO martingale that is not in BLO is constructed.

Article information

Tohoku Math. J. (2), Volume 69, Number 2 (2017), 183-194.

First available in Project Euclid: 24 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G46: Martingales and classical analysis
Secondary: 60G42: Martingales with discrete parameter 42B35: Function spaces arising in harmonic analysis

Martingale BMO BLO pointwise multiplier Campanato space


Nakai, Eiichi; Sadasue, Gaku. Some new properties concerning BLO martingales. Tohoku Math. J. (2) 69 (2017), no. 2, 183--194. doi:10.2748/tmj/1498269622.

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  • C. Bennett, Another characterization of BLO, Proc. Amer. Math. Soc. 85 (1982), 552–556.
  • R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249–254.
  • H. Lin, E. Nakai and D. Yang, Boundedness of Lusin-area and $g_{\lambda}^{\ast}$ functions on localized BMO spaces over doubling metric measure spaces, Bull. Sci. Math. 135 (2011), 59–88.
  • R. L. Long, Martingale spaces and inequalities, Peking University Press, Beijing, 1993.
  • E. Nakai, A generalization of Hardy spaces $H^p$ by using atoms, Acta Math. Sin. (Engl. Ser.) 24 (2008), 1243–1268.
  • E. Nakai and G. Sadasue, Martingale Morrey-Campanato spaces and fractional integrals, J. Funct. Spaces Appl. 2012 (2012), Article ID 673929, 29 pages. DOI:10.1155/2012/673929
  • E. Nakai and G. Sadasue, Pointwise multipliers on martingale Campanato spaces, Studia Math. 220 (2014), 87–100.
  • A. Osȩkowski, Sharp estimates for functions of bounded lower oscillation, Bull. Aust. Math. Soc. 87 (2013), 68–81.
  • Y. Shiota, On a decomposition of BMO-martingales, Tohoku Math. J. (2) 33 (1981), 515–520.
  • Y. Shiota, Certain decompositions of BMO-martingales, Tohoku Math. J. (2) 33 (1981), 561–565.
  • N. Th. Varopoulos, A probabilistic proof of the Garnett-Jones theorem on BMO, Pacific J. Math. 90 (1980), 201–221.
  • N. Th. Varopoulos, The Helson-Szegö theorem and $A_p$-functions for Brownian motion and several variables, J. Funct. Anal. 39 (1980), 85–121.
  • F. Weisz, Martingale Hardy spaces and their applications in Fourier analysis, Lecture Notes in Mathematics, 1568, Springer-Verlag, Berlin, 1994.