Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces

We establish an interpolation result for the rearrangement-invariant martingale Hardy spaces. By using this interpolation result, we extend the mapping properties of the martingale transforms and the fractional integrals on martingale function spaces. In particular, we obtain the mapping properties on the martingale Hardy–Orlicz spaces, the grand martingale Hardy spaces and the martingale Hardy–Lorentz–Karamata spaces. Copyright © 2020 Akadémiai Kiadó, Budapest, Hungary.