Wavelet Characterizations of Variable Anisotropic Hardy Spaces

Let p(<middle dot>): & Ropf;n -> (0, infinity] be a variable exponent function satisfying the globally log-H & ouml;lder continuous condition and A a general expansive matrix on & Ropf;n. Let HAp(<middle dot>)(& Ropf;n) be the variable anisotropic Hardy space associated with A. In this paper, via first establishing a criterion for affirming some functions being in the space HAp(<middle dot>)(& Ropf;n), the authors obtain several equivalent characterizations of HAp(<middle dot>)(& Ropf;n) in terms of the so-called tight frame multiwavelets, which extend the well-known wavelet characterizations of classical Hardy spaces. In particular, these wavelet characterizations are shown without the help of Peetre maximal operators.