Integrability of the Fourier transform via Riesz derivative

Abstract A known condition for the integrability of the one-dimensional Fourier transform, in which the derivative is assumed to belong to the real Hardy space, is extended to the $n$ -dimensional case, in terms of the $n$ -th Riesz derivative. We obtain results for the Riesz derivatives of other orders. The function spaces involved in this study are compared and analyzed.