We consider several real-time scheduling problems on heterogeneous multiprocessor platforms, in which the different processors share a common memory pool. These include (i)~scheduling a collection of implicit-deadline sporadic tasks with the objective of meeting all deadlines; and (ii)~scheduling a collection of independent jobs with the objective of minimizing the makespan of the schedule. Both these problems are intractable (NP-hard). For each, we derive polynomial-time algorithms for solving them approximately, and show that these algorithms have bounded deviation from optimal behavior. We also consider the problem of determining how much common memory a platform needs in order to be able to accommodate a specified real-time workload.