Real Interpolation Between Strong Martingale Hardy Spaces

Abstract

In this paper, we establish a decomposition theorem for strong martingale Hardy space \(sH_p^\sigma \), which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between \(sH_p^\sigma \;(0<p\le 1)\) and \(sL_2\). Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given.