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

Let $\mathrm{\Phi }$ be a Young function. We study convolution properties for symbol classes $s_{A,\mathrm{\Phi }}$, which consist of all $a$ such that the pseudo-differential operator ${\mathrm{Op}}_A(a)$ is in the Orlicz Schatten class ${\mathcal{I}}_{\mathrm{\Phi }}(L^2({\mathbf{R}}^d))$. Especially we prove Young type results for such classes. We apply the results on Toeplitz operators and prove Orlicz Schatten properties of such operators.