Let \(\Gamma=\{y\in \mathbb{R}^n: y_n>(y^2_1+ \cdots+y^2_{n-1})^{1/ 2}\}\) be the future light cone, \(\Omega=\mathbb{R}^n+i\Gamma\) be the associated tube domain, and \(Q(z)= -z^2_1- \cdots-z^2_{n-1} +z_n^2\) be the Lorentz quadratic form. The weighted Bergman space \(A^p_0\) is the closed subspace of \(L^p_\nu =L^p (\Omega,Q(y)^{\nu-n} dxdy)\) consisting of holomorphic functions. The weighted Bergman kernel \(B_\nu(z,w)= c_\nu Q(z- \overline w)^{-\nu}\) is the reproducing kernel on \(A^2_\nu\), and the weighted Bergman projection \[ P_\nu f(z)=\int_\Omega f(u+iv) B_\nu(z,u+iv) Q(\nu)^{\nu-n}dudv \] is the orthogonal projection of \(L^2_\nu\) onto \(A^2_\nu\).
Using technique of mixed norm spaces and Laplace-Fourier transforms, the authors prove that the operator \(P_\nu\) is bounded on \(L^p_\nu\) if \[ 1+{n-2\over 2(\nu-1)}< p<1+{2(\nu-1)\over n-2}. \]