k=1 Applying Theorem 5, we conclude that f ∈ b1,ϑ(Bn), where ϑ = p + 2α − 2. The proof of the Corollary is complete. □ Acknowledgements. We thank the referee for providing constructive comments and help in improving this paper. This research was partly supported by the National Natural Science Foundation of China (No. 11571216 and No. 11401184), the Science and Technology Plan Project of Hunan Province (No. 2016TP1020), the Science and Technology Plan Project of Hengyang City (2017KJ183), and Hunan Province double First-class Construction Application characteristic discipline Project (Xiangjiaotong [2018] 469).