On the Multilinear Fractional Transforms

Abstract

In this paper we first introduce multilinear fractional wavelet transform on R-n x R-+(n) using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff-Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.