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Fourier multipliers and weak differential subordination of martingales in UMD Banach spaces
We introduce the notion of weak differential subordination for martingales, and show that a Banach space $X$ is UMD if and only if for all $p\in (1,\infty)$ and all purely discontinuous $X$-valued martingales $M$ and $N$ such that $N$ is weakly differenti