Real-variable characterizations of local Orlicz-slice Hardy spaces with application to bilinear decompositions

Abstract

Recently, both the bilinear decompositions [Formula: see text] and [Formula: see text] were established. In this paper, the authors prove in some sense that the former is sharp, while the latter is not. To this end, the authors first introduce the local Orlicz-slice Hardy space which contains [Formula: see text], a variant of the local Orlicz Hardy space, introduced by Bonami and Feuto as a special case, and obtain its dual space by establishing its characterizations via atoms, finite atoms, and various maximal functions, which are new even for [Formula: see text]. The relationship [Formula: see text] is also clarified.