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.
"Atomic decomposition of martingale weighted Lorentz spaces with two-parameter and applications." Rocky Mountain J. Math. 47 (3) 927 - 945, 2017. https://doi.org/10.1216/RMJ-2017-47-3-927