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Multicore processors can deliver higher performance than single-core processors by exploiting thread level parallelism (TLP): applications are split into independent threads, each of which is mapped into a different core, reducing the execution time and potentially its worst-case execution time (WCET). Unfortunately, inter-thread interferences generated by simultaneous accesses to shared resources from different threads may completely destroy the performance benefits brought by TLP. This paper proposes a software/hardware cache partitioning approach that reduces the inter-thread memory interferences generated in hard real-time software-pipelined parallel applications. Our results show that our approach effectively reduces memory interferences, while still guaranteeing a predictable timing behaviour, achieving a WCET estimation reduction of 28% for a software pipelined version of the LU decomposition application with respect to the single-threaded version.