We establish a new characterization of AUMD （analytic unconditional martingale differences） spaces via biplurisubharmonic functions. That is, B∈AUMD iff there exists a bpsbh （biplurisubharmonic） function L ： B &...We establish a new characterization of AUMD （analytic unconditional martingale differences） spaces via biplurisubharmonic functions. That is, B∈AUMD iff there exists a bpsbh （biplurisubharmonic） function L ： B × B→[-∞,∞） satisfying L（x,0）, L（0,y）≥L（0,0）〉0,L（x,y）≤L（0,0）＋｜x-y｜ and L（x,y）≤｜x-y｜ for ｜x＋y｜＋｜x-y｜≥1. This provides an analogue of Piasecki＇s characterization of AUMS spaces. Our arguments are based on some special properties of zigzag analytic martingales and martingale transforms.展开更多
基金Supported by the National Natural Science Foun-dation of China (10371093)
文摘We establish a new characterization of AUMD （analytic unconditional martingale differences） spaces via biplurisubharmonic functions. That is, B∈AUMD iff there exists a bpsbh （biplurisubharmonic） function L ： B × B→[-∞,∞） satisfying L（x,0）, L（0,y）≥L（0,0）〉0,L（x,y）≤L（0,0）＋｜x-y｜ and L（x,y）≤｜x-y｜ for ｜x＋y｜＋｜x-y｜≥1. This provides an analogue of Piasecki＇s characterization of AUMS spaces. Our arguments are based on some special properties of zigzag analytic martingales and martingale transforms.
