Boundedness of Bergman projections on tube domains over light cones

Let Gamma be the future light cone in R-n, and Omega = R-n + i Gamma be the associated tube domain. We prove that the weighted Bergman projection P-v P(v)f(z) = integral (Omega) f(w)Q(z-(w) over bar)(-v) Q((s) over tilde)(v-n ) dw is bounded on L-p(Omega, Q(v-n)((s) over tilde )dw) for 1 + n-2 / 2(v-1) < 1 + 2(v-1) / n-2, where Q denotes the Lorentz quadratic form. This theorem extends previous results by Bekolle and Bonami [BB]. Our proof relies on th e analysis of the projection P-v on mixed norm spaces, which allows us to e xploit the oscillation of the Bergman kernel using the Laplace-Fourier tran sform.