Interpolation on weak martingale Hardy-type spaces associated with quasi-Banach function lattice

Abstract

We study the real interpolation spaces between weak martingale Hardy-type spaces \(WH_{X}^{s}(\Omega)\) and martingale Hardy space \(H_{\infty}^{s}(\Omega)\) associated with quasi-Banach function lattice by using atomic characterizations of weak martingale Hardy-type spaces. As applications, we obtain the corresponding results on the weighted Lorentz space and the generalized grand Lebesgue space. We point out that even in these special cases, the results obtained in this article are also new.