The UMD property for musielak–orlicz spaces

In this paper we show that Musielak–Orlicz spaces are UMD spaces under the so-called Δ₂ condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak–Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that...