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An upper bound for the $L^2$- norm of the Euler class $e(\cal F)$ of anarbitrary transversally orientable foliation $\cal F$ of codimension one,defined on a three-dimensional closed irreducible orientable Riemannian3-manifold $M^3$ is given in terms of constants bounding the volume, the radiusof injectivity, the sectional curvature of $M^3$ and the modulus of meancurvature of the leaves. As a consequence we get that only finitely manycohomolo\-gical classes of the group $H^2(M^3)$ that can be realized by theEuler class $e(\cal F)$ of a two-dimensional transversely oriented foliation$\cal F $ whose leaves have the modulus of mean curvature which is boundedabove by the fixed constant $H_0$.

$L^2$-norm of the Euler class for foliations on closed irreducible Riemannian 3-Manifolds