Bilinear decompositions of products of local Hardy and Lipschitz or BMO spaces through wavelets

Abstract

Let [Formula: see text] and [Formula: see text] be the local Hardy space in the sense of D. Goldberg. In this paper, the authors establish two bilinear decompositions of the product spaces of [Formula: see text] and their dual spaces. More precisely, the authors prove that [Formula: see text] and, for any [Formula: see text], [Formula: see text], where [Formula: see text] denotes the local BMO space, [Formula: see text], for any [Formula: see text] and [Formula: see text], the inhomogeneous Lipschitz space and [Formula: see text] a variant of the local Orlicz–Hardy space related to the Orlicz function [Formula: see text] for any [Formula: see text] which was introduced by Bonami and Feuto. As an application, the authors establish a div-curl lemma at the endpoint case.