Weighted mixed-norm inequality on Doob's maximal operator and John–Nirenberg inequalities in Banach function spaces

W. CHEN, Kwok Pun Victor HO, Y. JIAO, D. ZHOU

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Abstract

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.
Original languageEnglish
Pages (from-to)408-433
JournalActa Mathematica Hungarica
Volume157
Issue number2
Early online dateDec 2018
DOIs
Publication statusPublished - Apr 2019

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Citation

Chen, 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

Keywords

  • Mixed-norm inequality
  • Weight
  • Doob's maximal operator
  • Extrapolation
  • BMO