The Cardinality of Sumsets: Different Summands

Let $h$ be a positive integer and $A,B_1,B_2,\dots ,B_h$ be finite sets in a commutative group. We bound $\mathrm{\mid }A+B_1+\mathrm{.}\mathrm{.}\mathrm{.}+B_h\mathrm{\mid }$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$and$h$. Extremal examples, which demonstrate that the bound is asymptotically sharp in all the parameters, are furthermore provided.