Bibloch mappings and composition operators from Bloch type spaces to BMOA. (English) Zbl 1222.30045
The paper constructs analytic functions \(f_1\) and \(f_2\) on the unit disk \(\mathbb D\) such that
\[
|f_1'(z)|+|f_2'(z)|\sim\psi\left(1\over{1-|z|}\right)
\]
for a wide class of weight functions \(\psi\). As applications, several known results about Bloch-BMO pullbacks are generalized.
Reviewer: Kehe Zhu (Albany)
References:
| [1] | Blasco, O.; De Souza, G. S., Spaces of analytic functions on the disc where the growth of \(M_p(F, r)\) depends on a weight, J. Math. Anal. Appl., 147, 2, 580-598 (1990) · Zbl 0712.30043 |
| [2] | Galanopulos, P., On \(B_{\log}\) to \(Q_{\log}^p\) pullbacks, J. Math. Anal. Appl., 337, 712-725 (2008) · Zbl 1137.30015 |
| [3] | Gauthier, P. M.; Xiao, J., BiBloch-type maps: existence and beyond, Complex Var. Theory Appl., 47, 8, 667-678 (2002) · Zbl 1026.30035 |
| [4] | Li, Haiying; Liu, Peide, Composition operators between generally weighted Bloch space and \(Q_{\log}^q\) space, Banach, J. Math. Anal., 3, 1, 99110 (2009) · Zbl 1163.47019 |
| [5] | Havin, V. P., On the factorization of holomorphic functions smooth up to the boundary, Zap. Nauchn. Sem. LOMI, 22, 202-205 (1971), (in Russian) · Zbl 0271.30032 |
| [6] | Kwon, E. G., Hyperbolic \(g\)-function and Bloch pullback operators, J. Math. Anal. Appl., 309, 626-637 (2005) · Zbl 1088.30029 |
| [7] | Mateljević, M.; Pavlović, M., \(L^p\) behaviour of the integral means of analytic functions, Studia Math., 77, 219-237 (1984) · Zbl 1188.30004 |
| [8] | Pavlović, M., Lipschitz spaces and spaces of harmonic functions in the unit disc, Michigan Math. J., 35, 2, 301-311 (1988) · Zbl 0689.31001 |
| [9] | Pavlović, M., On the moduli of continuity of \(H^p\)-functions with \(0 < p < 1\), Proc. Edinb. Math. Soc. (2), 35, 1, 89-100 (1992) · Zbl 0754.30029 |
| [10] | Pavlović, M., Mixed norm spaces of analytic and harmonic functions. I, Publ. Inst. Math. (Beograd) (N.S.), 40, 54, 117-141 (1986) · Zbl 0619.46022 |
| [11] | Ramey, W.; Ullrich, D., Bounded mean oscillation of Bloch pull-backs, Math. Ann., 291, 591-606 (1991) · Zbl 0727.32002 |
| [12] | Shields, A. L.; Williams, D. L., Bounded projections, duality, and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc., 162, 287-302 (1971) · Zbl 0227.46034 |
| [13] | Shields, A. L.; Williams, D. L., Bounded projections, duality, and multipliers in spaces of harmonic functions, J. Reine Angew. Math., 299/300, 265-279 (1978) · Zbl 0367.46053 |
| [14] | Shields, A. L.; Williams, D. L., Bounded projections and the growth of harmonic conjugates in the unit disc, Michigan Math. J., 29, 3-25 (1982) · Zbl 0508.31001 |
| [15] | Xiao, J., Holomorphic \(Q\) Classes, Lecture Notes in Math., vol. 1767 (2001), Springer · Zbl 0983.30001 |
| [16] | Zygmund, A., Trigonometric Series, vols. I, II (1959), Cambridge University Press: Cambridge University Press New York · Zbl 0085.05601 |
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