On a class of lacunary series in BMOA. (English) Zbl 1137.32301
Summary: We consider a special class of lacunary series and we characterize their membership in the BMOA of the unit ball of \(\mathbb C^n\) in terms of their Taylor coefficients. In addition, we show that a similar result holds for the class VMOA.
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 11B83 | Special sequences and polynomials |
References:
| [1] | Girela, Daniel, Analytic functions of bounded mean oscillation, (Aulaskary, R., Complex Function Spaces. Complex Function Spaces, Univ. Joensuu Dept. Math. Rep. Ser., vol. 4 (2001), University of Joensuu: University of Joensuu Finland), 61-170 · Zbl 0981.30026 |
| [2] | Hedenmalm, Haakan; Korenblum, Boris; Zhu, Kehe, Theory of Bergman Spaces (2000), Springer-Verlag: Springer-Verlag New York · Zbl 0955.32003 |
| [3] | Jevtic, Miroljub, On the Carleson measure characterization of BMOA functions on the ball, Proc. Amer. Math. Soc., 114, 379-386 (1992) · Zbl 0752.32003 |
| [4] | Rudin, Walter, Function Theory in the Unit Ball of \(C^n (1980)\), Springer-Verlag: Springer-Verlag New York · Zbl 0495.32001 |
| [5] | Hasi Wulan, Kehe Zhu, Bloch and BMO functions in the unit ball, Complex Variables, in press; Hasi Wulan, Kehe Zhu, Bloch and BMO functions in the unit ball, Complex Variables, in press · Zbl 1157.32004 |
| [6] | Zhu, Kehe, Spaces of Holomorphic Functions in the Unit Ball (2005), Springer-Verlag: Springer-Verlag New York · Zbl 1067.32005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
