bound on a sum of Poisson random variables

Question

Let $X_i$ be Poisson random variables, i.e. $P(X=k)=e^{-\lambda}\frac{\lambda^k}{k!}, \quad k=0,1,2,...$. Let $X=\sum_{i=0}^ny_iX_i$, with $y_i\in R, \quad i=0,... n$ and let $r\geq 1$.

Is there an inequality of type: $$ E(|X|^r)\leq Cf(y_i)g(X_i)? $$