Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus (Q1599925)

The paper concerns symbols \(a(x,\eta)\) such that the corresponding Weyl pseudodifferential operator \(a^w(x,D)\) is of Schatten-von Neumann class of order \(p\), \(p\geq 1\), on \(L^2\). The theory here is actually formulated in the framework of twisted convolution algebras so that one can read it independently of the pseudodifferential setting. Several results are given describing in particular when \(a(x,\eta)\) belongs to certain Besov or Sobolev spaces. Finally, an application to Toeplitz operators is presented.