LITTLEWOOD–PALEY CHARACTERIZATIONS OF ANISOTROPIC WEAK MUSIELAK–ORLICZ HARDY SPACES

Let be an expansive dilation on and an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations in terms of the anisotropic Lusin-area function, -function or -function, respectively. All these characterizations for anisotropic weak Hardy spaces (namely, for all and with ) are new. Moreover, the range of in the anisotropic -function characterization of coincides with the best known range of the -function characterization of classical Hardy space or its weighted variants, where .