The boundedness of parametrized Littlewood-Paley operators and their commutators on grand variable Morrey-Herz spaces TAO Wenwen CHEN Xijuan LU Guanghui*

Using the definition of the grand variable Herz-Morrey spaces, Minkowski’s inequality, Hölder’s inequality, and previous results, we prove the boundedness of the parametrized area integral and the Littlewood-Paley g_\delta ^\ast -function. We also establish the boundedness of their higher order commutators, which are generated by BMO space, on these spaces.