Martingale inequalities and fractional integral operator in variable Hardy-Lorentz spaces

Abstract

Let (Ω,F,P) be a complete probability space. We introduce variable Lorentz space Lp(⋅),q(Ω) defined by rearrangement functions and its related properties. Then, we establish martingale inequalities among these martingale Hardy-Lorentz spaces Hp(⋅),q(Ω) by applying the interpolation theorem. Furthermore, we study the boundedness of the fractional integral operator in variable martingale Hardy spaces Hp(⋅)M(Ω) and Hp(⋅),qM(Ω).