Bounded projectors on $L^p$ spaces in the unit ball

The paper studies the linear operators depending on normal pair of weight functions $\{\varphi,\psi\}$ in the Banach spaces $L^p(B)$. Here $B$ is the unit ball in the complex space $\mathbb{C}_n$. In particular, we study the question: for which values of $p$ these operators are bounded projectors.