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Sharp continuity results for the short-time Fourier transform and for localization operators

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Abstract

We completely characterize the boundedness on Wiener amalgam spaces of the short-time Fourier transform (STFT), and on both L p and Wiener amalgam spaces of a special class of pseudodifferential operators, called localization operators. Precisely, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces W(L p, L q) are given and their sharpness is shown. Localization operators are treated similarly: using different techniques from those employed in the literature, we relax the known sufficient boundedness conditions for these operators to be bounded on L p spaces and prove the optimality of our results. Next, we exhibit sufficient and necessary conditions for such operators to be bounded on Wiener amalgam spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    Elena Cordero

  2. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Fabio Nicola

Authors
  1. Elena Cordero
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  2. Fabio Nicola
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Corresponding author

Correspondence to Fabio Nicola.

Additional information

Communicated by K. Gröchenig.

F. Nicola was partially supported by the Progetto MIUR Cofinanziato 2007 Analisi Armonica.

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Cordero, E., Nicola, F. Sharp continuity results for the short-time Fourier transform and for localization operators. Monatsh Math 162, 251–276 (2011). https://doi.org/10.1007/s00605-010-0210-3

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  • DOI: https://doi.org/10.1007/s00605-010-0210-3

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