  The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the
Hilbert function of algbebras with the Lefschetz property. We extend this
characterization to algebras with the Lefschetz property m times. We also give
upper bounds for the Betti numbers of Artinian algebras with a given Hilbert
function and with the Lefschetz property m times and describe the cases in
which these bounds are reached.
