Orlicz-Lorentz Hardy martingale spaces

Abstract

Martingale Hardy spaces are widely studied in the field of mathematical physics and probability. In this paper, we develop the theory of Orlicz-Lorentz Hardy martingale spaces, which are much more wider than the classical Lorentz Hardy martingale spaces. More precisely, we first investigate several basic properties of Orlicz-Lorentz spaces, and then construct the atomic decomposition theorems of these martingale function spaces. Also, we establish the dual theorem of Orlicz-Lorentz Hardy spaces for martingales. Furthermore, we study the boundedness of generalized fractional integral operators Iϕ in this new framework, where ϕ is a non-negative concave function. The results partially extend the very recent results Jiao et al. (2017) [21].