Multiplier Theorems for the Short-Time Fourier Transform

Abstract

So-called short-time Fourier transform multipliers (also called Anti-Wick operators in the literature) arise by applying a pointwise multiplication operator to the STFT before applying the inverse STFT. Boundedness results are investigated for such operators on modulation spaces and on L p -spaces. Because the proofs apply naturally to Wiener amalgam spaces the results are formulated in this context. Furthermore, a version of the Hardy-Littlewood inequality for the STFT is derived.