The condition mentioned in the title is equivalent to the representability of f as the quotient f = v 1 /v 2, where v 1 and v 2 obey the inequalities |R j v i | ≤ cv i , i = 1, 2, j = 1, . . . , n. Here R 1 , . . . , R n are the Riesz transformations. Bibliography: 3 titles.
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J. Garcia-Cuerva and J. L. Rubio de Francia, Weigthed Norm Inequalities and Related Topics, North-Holland (1985).
S. V. Kislyakov and T. W. Gamelin, “Uniform algebras as Banach spaces,” in: W. B. Johnson and J. Lindedstrauss (eds.), Handbook of Banach Spaces, Elsevier Science (2001).
W. Hayman and P. Kennedy, Subharmonic Functions, Academic Press (1989).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 416, 2013, pp. 59–69.
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Vasilyev, I.M. The Property log(f) ∈ BMO(ℝn) in Terms of Riesz Transforms. J Math Sci 202, 519–525 (2014). https://doi.org/10.1007/s10958-014-2058-x
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DOI: https://doi.org/10.1007/s10958-014-2058-x