Real interpolation between martingale Hardy and BMO spaces
The usual interpolation space \((A_0,A_1)_{\theta,q}\) is defined as the space of all functions \(f\) in \(A_0+A_1\) for which \[ { \| f \|}_{{(A_0,A_1)}_{\theta ,q}}:= \left( \int_0^\infty \left(t^{- \theta}K(t,f,A_0,A_1) \right) ^q \, {{dt} \over {t}} \right)^{1/q} < \infty \] where \(K(t,f,A_0,A_1) := \inf_{f=f_0+f_1} \left\{ \|f_0\|_{A_0} + t\|f_1\|_{A_1} \right\}\), \(0< \theta <1\) and \(0<q \leq \infty \). In this paper interpolation spaces defined by a function parameter \(\varphi\) are investigated. Here \[ { \| f \|}_{{(A_0,A_1)}_{\varphi ,q}}:= \left( \int_0^\infty \left(\frac{K(t,f,A_0,A_1)}{\varphi(t)} \right) ^q \, {{dt} \over {t}} \right)^{1/q} \] with a suitable function \(\varphi\). The interpolation spaces between martingale Hardy and \(BMO\) spaces are characterized.
scientific article; zbMATH DE number 6146287
scientific article