ATOMIC DECOMPOSITION OF MARTINGALE WEIGHTED LORENTZ SPACES WITH TWO-PARAMETER AND APPLICATIONS

摘要

We introduce martingale weighted two parameter Lorentz spaces and establish atomic decomposition theorems. As an application of atomic decomposition we obtain a sufficient condition for sublinear operators defined on martingale weighted Lorentz spaces to be bounded. Moreover, some interpolation properties with a function parameter of those spaces are obtained.