Complex interpolation between noncommutative martingale BMO spaces and Hardy–Orlicz spaces

Let \(\mathcal {M}\) be a semifinite von Neumann algebra and \((\mathcal {M}_n)_{n\ge 0}\) a nondecreasing filtration of von Neumann subalgebras of \(\mathcal {M}\). Suppose that \(\Phi \) is a p-convex and q-concave Orlicz function with \(1< p\le q <\infty \). In this paper, we establish the complex interpolation between the column martingale little BMO space \(\textrm{bmo}^c(\mathcal {M})\) and the noncommutative column conditioned martingale Hardy–Orlicz space \(h_{\Phi }^c(\mathcal {M})\) associated with the filtration \((\mathcal {M}_n)_{n\ge 0}\).