Convolutions of Orlicz spaces and Orlicz Schatten classes, with applications to Toeplitz operators

Let Φ Φ be a Young function. We study convolution properties for symbol classes sA,Φ s A , Φ , which consist of all a such that the pseudo-differential operator OpA(a) Op A ( a ) is in the Orlicz Schatten class I_Φ (L²(Rᵈ)) I Φ ( L 2 ( R d ) ) . Especially we prove Young type results for such classes. We apply the results to Toeplitz operators and prove Orlicz Schatten properties of such operators.