Wavelet Characterizations of Variable Anisotropic Hardy Spaces

Abstract

Let p(·): ℝⁿ → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on ℝⁿ. Let H ^p(·)_A (ℝⁿ) 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 H ^p(·)_A (ℝⁿ), the authors obtain several equivalent characterizations of H ^p(·)_A (ℝⁿ) 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.