Borcherds Products on Unitary Group $U(2,1)$

In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp $\mathrm{\infty }$ for ${\mathrm{\Gamma }}_0(4)$ of integral weight $k$ for $k\le -1$, and we make use of the basis elements for the case $k=-1$ to construct explicit Borcherds products on unitary group $U(2,1)$.