摘要 : Let p(.) : R-n -> (0, infinity] be a variable exponent function satisfying the globally log-Holder continuous condition and A a general expansive matrix on R-n. In this article, the authors first introduce the variable anisotro... 展开 Let p(.) : R-n -> (0, infinity] be a variable exponent function satisfying the globally log-Holder continuous condition and A a general expansive matrix on R-n. In this article, the authors first introduce the variable anisotropic Hardy space H-A(p(.))(R-n) associated with A, via the non-tangential grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain various equivalent characterizations of H-A(p(.))(R-n), respectively, by means of atoms, finite atoms, the Lusin area function, the Littlewood-Paley g-function or g(lambda)*-function. As applications, the authors first establish a criterion on the boundedness of sublinear operators from H-A(p(.))(R-n) into a quasi-Banach space. Then, applying this criterion, the authors show that the maximal operators of the Bochner-Riesz and the Weierstrass means are bounded from H-A(p(.))(R-n) to L-p(.)(R-n) and, as consequences, some almost everywhere and norm convergences of these Bochner-Riesz and Weierstrass means are also obtained. These results on the Bochner-Riesz and the Weierstrass means are new even in the isotropic case. 收起