We prove a weighted mixed-norm inequality for the Doob maximal operator on a filtered measure space. We also give some characterizations of martingale BMO spaces in the setting of Banach function spaces. The main method is based on the technique of extrapolation on martingale Banach spaces. Copyright © 2018 Akadémiai Kiadó, Budapest, Hungary.
CitationChen, W., Ho, K.-P., Jiao, Y., & Zhou, D. (2019). Weighted mixed-norm inequality on Doob's maximal operator and John–Nirenberg inequalities in Banach function spaces. Acta Mathematica Hungarica, 157(2), 408-433. doi: 10.1007/s10474-018-0889-5
- Mixed-norm inequality
- Doob's maximal operator