A New Molecular Characterization Of Diagonal Anisotropic Musielak-Orlicz Hardy Spaces

Anisotropy is a common attribute of the nature,which shows different characteriza-tions in different directions of all or part of the physical or chemical properties of an ob-ject.In this paper,we study the boundedness of the function space and its associated oper-ators in the case of diagonal anisotropy.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 study to be the molecular characterization of Musielak-Orlicz Hardy space HDφ(Rn).As an application,the authors obtain the boundedness of a new class of general integral anisotropic Calderon-Zygmund operators from HDφ(Rn)to Lφ(Rn)or from HDφ(Rn)to itself.