Edit,this is the exact phrasing of my question Let $\lambda\in\mathbb{R^n}$.Prove that $f\star_{\lambda}g\in L^2(\mathbb{C^n})$ for all functions $f$ and $g$ in $L^2(\mathbb{C^n})$.What Happens when $\lambda=0?$ I been reading the book Harmonic Analysis on the Heisenberg Group By Sundaram Thang...