REAL-VARIABLE CHARACTERIZATIONS OF NEW ANISOTROPIC MIXED-NORM HARDY SPACES

摘要

Let (p)over-right-arrow is an element of (0, infinity)(n) and A be a general expansive matrix on R-n. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces H-A((p)over-right-arrow)(R-n) associated with A and then establish their radial or non-tangential maximal function characterizations. Moreover, the authors characterize H-A((p)over-right-arrow)(R-n), respectively, by means of atoms, finite atoms, Lusin area functions, Littlewood-Paley g-functions or g(lambda)*-functions via first establishing an anisotropic Fefferman-Stein vector-valued inequality on the mixed-norm Lebesgue space L(p)over-right-arrow(R-n) . In addition, the authors also obtain the duality between H-A((p)over-right-arrow)(R-n) and the anisotropic mixed-norm Campanato spaces. As applications, the authors establish a criterion on the boundedness of sublinear operators from H-A((p)over-right-arrow)(R-n) into a quasi-Banach space. Applying this criterion, the authors then obtain the boundedness of anisotropic convolutional delta-type and non-convolutional beta-order Calderon-Zygmund operators from H-A((p)over-right-arrow)(R-n) to itself [or to L(p)over-right-arrow(R-n)]. As a corollary, the boundedness of anisotropic convolutional delta-type Calderon-Zygmund operators on the mixed-norm Lebesgue space L(p)over-right-arrow(R-n) with (p)over-right-arrow is an element of (1, infinity)(n) is also presented.