We study continuity properties for a family {s_p}_p1 of increasing Banach algebras under the twisted convolution, which also satisfies that as_p, if and only if the Weyl operator a^w(x,D) is a Schatten–von Neumann operator of order p on L². We discuss inclusion relations between the s_p-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on s_p for dilated convolution. As an application we prove that f(a)s₁, when as₁ and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.