鞅极大算子的强弱(φ1，φ2)-型不等式

On the Strong and Weak (φ_1,φ_2)-Type Inequalities for Maximal Operator in Martingale Spaces

研究了鞅Orlicz空间极大算子的双φ-不等式,得到了相应不等式成立的一些充要条件,给出了Burkholder-Gundy型双φ-不等式的等价条件,讨论了鞅的Cianchi弱(φ_1,φ_2)-型不等式与φ-函数的强于关系的联系.

This paper studies the two φ-inequalities for maximal operator in Orlicz martingale spaces. The sufficient and necessary conditions on the inequalities corresponding are obtained. The equivalent conditions on Burkholder-Gundy＇s two G-inequalities are also given. Finally, the relation of Cianchi＇s weak （φ1, φ2）-type inequality and the stronger order of φ-functions is discussed.