ESTIMATES FOR UNIMODULAR FOURIER MULTIPLIERS ON MODULATION SPACES

By Akihiko Miyachi, Fabio Di Nicola, S. Rivetti, A. Tabacco, Naohito Tomita. 2009

73 citations recorded by the source corpus.

We study the action on modulation spaces of Fourier multipliers with symbols e^iμ(ξ), for real-valued functions μ having unbounded second derivatives. In a simplified form our result reads as follows: if μ satisfies the usual symbol estimates of order α ≥ 2, or if μ is a positively homogeneous function of degree α, then the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces M^{p,q}_s and M^{p,q}, for all 1 ≤ p, q ≤ ∞ and s ≥ (α − 2)n|1/p − 1/2|. Here s represents the loss of derivatives. The above threshold is shown to be sharp for any homogeneous function μ whose Hessian matrix is non-degenerate at some point

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c8bcefc25767c07b74aef603d7b40e506891f06

Citations in the corpus

• The inclusion relation between Sobolev and modulation spaces (2010, unknown): “Theorem C (Miyachi-Nicola-Rivetti-Tabacco-Tomita [12]).”