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Real Interpolation Between Strong Martingale Hardy Spaces
Kaituo Liu
,
Jianzhong Lu
,
Lihua Peng
Abstract
In this paper, we establish a decomposition theorem for strong martingale Hardy space $sH^{\sigma}_p$, which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between $sH^{\sigma}_p $ $(0 < p \leq 1)$ 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.