Modulation spaces, multipliers associated with the special affine Fourier transform

Abstract

We study some fundamental properties of the special affine Fourier transform (SAFT) in connection with the Fourier analysis and time-frequency analysis. We introduce the modulation space ${\mathbf{M}}_A^{r,s}$ in connection with SAFT and prove that if a bounded linear operator between new modulation spaces commutes with $A$-translation, then it is a $A$-convolution operator. We also establish Hörmander multiplier theorem and Littlewood-Paley theorem associated with the SAFT.

26 pages