Mining on Pegged Side Chains
Sidechains cannot create the same asset that is pegged to Bitcoins to use as a reward for mining. Obviously, it would be problematic if anyone could put in a certain amount of Bitcoins into a sidechain, and get out more/less than what was originally put in. 

However, there are many other ways to reward miners. Transaction fees is one example that is also used in Bitcoin. The sidechains paper lists some alternative reward mechanisms in section 6.1 such as demurrage (percentage of held coins are redistributed automatically to miners) and creation of a seperate unpegged asset on the side chain to reward miners.