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

Abstract

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.