Modulation Spaces, Multipliers Associated with the Special Affine Fourier Transform

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 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 Hormander multiplier theorem and Littlewood-Paley theorem associated with the SAFT.