Open AccessMartingale transforms on Banach function spaces
Author(s) -
Kwok Pun Victor Ho
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022114
Subject(s) - mathematics , lp space , interpolation space , pure mathematics , birnbaum–orlicz space , martingale (probability theory) , lorentz transformation , banach space , mathematical analysis , discrete mathematics , functional analysis , biochemistry , chemistry , physics , classical mechanics , gene
We establish the boundedness of martingale transforms on Banach function spaces by using the Rubio de Francia extrapolation theory and the interpolation theorem by Zygmund. The main result also yields the boundedness of the martingale transforms on rearrangement-invariant Banach function spaces, Orlicz spaces, Lorentz-Karamata spaces, Zygmund spaces, Lebesgue spaces with variable exponents, Morrey spaces with variable exponents and Lorentz-Karamata Morrey spaces.