Interpolation of Lorentz martingale spaces
The interpolation spaces are defined by a function parameter \(\varphi\), \[ { \| f \|}_{{(A_0,A_1)}_{\varphi ,q}}:= \left( \int_0^\infty \left(\frac{K(t,f,A_0,A_1)}{\varphi(t)} \right) ^q \, {{dt} \over {t}} \right)^{1/q} \] with a suitable function \(\varphi\), 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 \(0<q \leq \infty \). Similarly, Lorentz spaces and martingale Hardy-Lorentz spaces are introduced with the help of a function parameter. The interpolation spaces between different martingale Hardy-Lorentz spaces are characterized.
scientific article; zbMATH DE number 6131104
scientific article