2018/01/19 by Fabio Nicola, Eva Primo, Nicola, Fabio +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA
paper · pdf · doi:10.48550/arxiv.1801.06424
19 pages, 1 figure
arxiv created 2018/01/19 · arxiv updated 2018/01/22
We study the continuity on the modulation spaces Mp,q of Fourier multipliers with symbols of the type eiμ(ξ), for some real-valued function μ(ξ). A number of results are known, assuming that the derivatives of order ≥ 2 of the phase μ(ξ) are bounded or, more generally, that its second derivatives belong to the Sjöstrand class M∞,1. Here we extend those results, by assuming that the second derivatives lie in the bigger Wiener amalgam space W(F L1,L^∞); in particular they could have stronger oscillations at infinity such as cos |ξ|2. Actually our main result deals with the more general case of possibly unbounded second derivatives. In that case we have boundedness on weighted modulation spaces with a sharp loss of derivatives.