Products on Schatten-von Neumann classes and modulation spaces

2009/02/16 by Joachim Toft, Toft, Joachim
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0902.2654

openalex publication_date 2009/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider modulation space and spaces of Schatten-von Neumann symbols where corresponding pseudo-differential operators map one Hilbert space to another. We prove Hölder-Young and Young type results for such spaces under dilated convolutions and multiplications. We also prove continuity properties for such spaces under the twisted convolution, and the Weyl product. These results lead to continuity properties for twisted convolutions on Lebesgue spaces, e.g. L^p_(ω) is a twisted convolution algebra when 1≤ p≤ 2 and appropriate weight ω.

Related

• Twisted convolution, pseudo-differential operators and Fourier modulation spaces
• Continuity and Schatten properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces or Hörmander classes
• Multi-linear products with odd factors in pseudo-differential calculus with symbols in modulation spaces
• Convolutions of Orlicz spaces and Orlicz Schatten classes, with applications to Toeplitz operators
• Pseudo-differentialoperators on Orlicz modulation spaces