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.
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This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship No M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No K67642.
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Weisz, F. Multiplier Theorems for the Short-Time Fourier Transform. Integr. equ. oper. theory 60, 133–149 (2008). https://doi.org/10.1007/s00020-007-1546-5
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DOI: https://doi.org/10.1007/s00020-007-1546-5