Doob's inequality, Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces

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4 Citations (Scopus)

Abstract

We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces. Copyright © 2018 Wuhan Institute of Physics and Mathematics. Published by Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)93-109
JournalActa Mathematica Scientia
Volume38
Issue number1
Early online dateDec 2017
DOIs
Publication statusPublished - 2018

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martingales
Martingale Transform
Morrey Space
Martingale
Banach Function Space
function space
mathematics
Boundedness
Physics
Decompose
decomposition
physics

Citation

Ho, K.-P. (2018). Doob's inequality, Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces. Acta Mathematica Scientia, 38(1), 93-109. doi: 10.1016/S0252-9602(17)30119-4

Keywords

  • Morrey spaces
  • Banach function space
  • Block spaces
  • Doob's inequality
  • Burkholder-Gundy inequality
  • Martingale transform
  • Davis' decomposition
  • Martingale