A new molecular characterization of diagonal anisotropic Musielak-Orlicz Hardy spaces

Abstract

Let D:=diag(λ1,⋯,λn), where {λi}i=1n⊂C, be a diagonal anisotropic dilation on Rn with min1≤i≤n⁡|λi|>1 and let φ:Rn×[0,∞)→[0,∞) be an anisotropic growth function. In this article, the authors introduce the anisotropic Musielak-Orlicz Hardy space HDφ(Rn) via the grand maximal function and establish its molecular characterization via the atomic characterization of HDφ(Rn). As an application, the authors obtain the boundedness of a new class of general integral anisotropic Calderón-Zygmund operators from HDφ(Rn) to Lφ(Rn) or from HDφ(Rn) to itself.