Burkholder's inequalities associated with Orlicz functions in rearrangement invariant spaces

作者：Jiao, Yong; Quan, Xingyan; Wu, Lian^*

来源：Mathematische Zeitschrift, 2018, 289(3-4): 943-960.

DOI：10.1007/s00209-017-1982-0

• Martingales
• Burkholder's inequalities
• Orlicz functions
• Rearrangement invariant spaces

In this paper, we prove martingale inequalities associated with Orlicz functions in the framework of rearrangement invariant spaces. More precisely, let be an Orlicz function and let X be a rearrangement invariant spaces. We establish the new moment Burkholder inequalities when the Simonenko indices of and the Boyd indices of X satisfy some natural conditions. Our approach mainly relies on a new distribution estimate of the Davis type decomposition.

• 出版日期2018-8
• 单位中南大学