Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 47-57

LACUNARY SERIES AND Q_K SPACES ON THE UNIT BALL

Huaihui Chen and Wen Xu

Nanjing Normal University, Department of Mathematics
Nanjing 210097, P.R. China; hhchen 'at' njnu.edu.cn

University of Joensuu, Department of Physics and Mathematics
P.O. Box 111, FI-80101 Joensuu, Finland; wenxupine 'at' gmail.com

Abstract. In this paper, we establish a necessary condition for a kind of lacunary series on the unit ball to be in Q_K. As a consequence, we prove a necessary and sufficient condition for that Q_K coincides with the Bloch space. In the case of Q_p spaces we show that the condition, which is similar to that obtained by Hu, is also sufficient. This is a generalization of the result of Aulaskari, Xiao and Zhao for Q_p spaces on the unit disk.

2000 Mathematics Subject Classification: Primary 32A05, 32A37.

Key words: Lacunary series, Q_p spaces, Q_K spaces.

Reference to this article: H. Chen and W. Xu: Lacunary series and Q_K spaces on the unit ball. Ann. Acad. Sci. Fenn. Math. 35 (2010), 47-57.

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doi:10.5186/aasfm.2010.3503

LACUNARY SERIES AND QK SPACES ON THE UNIT BALL

Huaihui Chen and Wen Xu

LACUNARY SERIES AND Q_K SPACES ON THE UNIT BALL