Abstract
We obtain sharp reverse estimates for the logarithmic Bloch spaces on the unit disk. As an application, we study composition operators with values in the space BMOA.
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Abakumov E., Doubtsov E.: Reverse estimates in growth spaces. Math. Z. 271, 399–413 (2012)
Doubtsov E.: Bloch-to-BMOA compositions on complex balls, Proc. Amer. Math. Soc. 140, 4217–4225 (2012)
K. M. Dyakonov, Weighted Bloch spaces, H p, and BMOA, J. London Math. Soc. (2) 65 (2002), 411–417.
D. Girela, M. Pavlović, and J. Á. Peláez, Spaces of analytic functions of Hardy-Bloch type, J. Anal. Math. 100 (2006), 53–81.
Kwon E. G.: Composition of Blochs with bounded analytic functions, Proc. Amer. Math. Soc. 124, 1473–1480 (1996)
E. G. Kwon, Hyperbolic mean growth of bounded holomorphic functions in the ball, Trans. Amer. Math. Soc. 355 (2003), 1269–1294.
E. G. Kwon, Hyperbolic g-function and Bloch pullback operators, J. Math. Anal. Appl. 309 (2005), 626–637.
E. G. Kwon and M. Pavlović, Bi Bloch mappings and composition operators from Bloch type spaces to BMOA, J. Math. Anal. Appl. 382 (2011), 303–313.
Ramey W., Ullrich D.: Bounded mean oscillation of Bloch pull-backs . Math,Ann. 291, 591–606 (1991)
S. Yamashita, Hyperbolic Hardy class H 1, Math. Scand. 45 (1979), 261–266.
A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959.
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Petrov, A.N. Reverse estimates in logarithmic Bloch spaces. Arch. Math. 100, 551–560 (2013). https://doi.org/10.1007/s00013-013-0528-x
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DOI: https://doi.org/10.1007/s00013-013-0528-x