THE FOURIER TRANSFORM OF ANISOTROPIC HARDY SPACES WITH VARIABLE EXPONENTS AND THEIR APPLICATIONS

Let A be an expansive dilation on Rn , and p(??) : Rn ??? (0, ???) be a variable exponent function satisfying the globally log-H ??lder continuous condition. Let 3Ap(??) (Rn) be the variable anisotropic Hardy space introduced by Liu [15]. In this paper, the authors obtain that the Fourier A (Rn) coincides with a continuous function F on Rn in the sense of tempered distributions. As applications, the authors further conclude a higher order convergence of the continuous function F at the origin and then give a variant of the Hardy-Littlewood inequality in the setting of anisotropic Hardy spaces with variable exponents.