Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give sev...Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.展开更多
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
文摘Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.
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.
