We study continuity properties for a family {s(p)} p greater than or equal to 1 of increasing Banach algebras under the twisted convolution, which also satisfies that a is an element of s(p), if and only if the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator of order p on L-2. We discuss inclusion relations between the s(p)-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f (a) is an element of s(1), when a is an element of s(1) 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. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.