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

Abstract Let $$\\Phi $$ Φ be a Young function. We study convolution properties for symbol classes $$s_{A,\\Phi }$$ s A , Φ , which consist of all a such that the pseudo-differential operator $$\\operatorname {Op}_A(a)$$ Op A ( a ) is in the Orlicz Schatten class $$\\mathscr {I}_\\Phi (L^2(\\textbf{R}^{d}))$$ 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.