Time-Frequency Analysis and PDE's

2009/01/01 by Anita Tabacco, Tabacco, Anita
Mathematics · #Advanced Harmonic Analysis Research #Fourier multipliers #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #modulation spaces #short-time Fourier transform

paper · doi:10.4230/dagsemproc.08492.10

openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the action on modulation spaces of Fourier multipliers with symbols e^imu(xi), for real-valued functions mu having unbounded second derivatives. We show that if mu satisfies the usual symbol estimates of order alphageq2, or if mu is a positively homogeneous function of degree alpha, the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces mathcalM^p,q_delta and mathcalM^p,q, for every 1leq p,qleqinfty and deltageq d(alpha-2)|frac1p-frac12|. Here delta represents the loss of derivatives. The above threshold is shown to be sharp for it all homogeneous functions mu whose Hessian matrix is non-degenerate at some point.

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