Lacunary series andQKspaces on the unit ball

Huaihui Chen, Wen Xu
2010 Annales Academiae Scientiarum Fennicae: Mathematica  
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. Let ν denote the Lebsegue measure on C m = R 2m , so normalized
more » ... 2m , so normalized that ν(B m ) = 1 and σ the normalized surface measure on S so that σ(S) = 1. Let dτ (z) = dν(z) (1 − |z| 2 ) m+1 , which is Möbius invariant.
doi:10.5186/aasfm.2010.3503 fatcat:bocn3ycgsrg5hpaqy5dazbjgje