While the accuracy of convolutional neural networks has achieved vast improvements by introducing larger and deeper network architectures, also the memory footprint for storing their parameters and activations has increased. This trend especially challenges power- and resource-limited accelerator designs, which are often restricted to store all network data in on-chip memory to avoid interfacing energy-hungry external memories. Maximizing the network size that fits on a given accelerator thus requires to maximize its memory utilization. While the traditionally used ping-pong buffering technique is mapping subsequent activation layers to disjunctive memory regions, we propose a mapping method that allows these regions to overlap and thus utilize the memory more efficiently. This work presents the mathematical model to compute the maximum activations memory overlap and thus the lower bound of on-chip memory needed to perform layer-by-layer processing of convolutional neural networks on memory-limited accelerators. Our experiments with various real-world object detector networks show that the proposed mapping technique can decrease the activations memory by up to 32.9%, reducing the overall memory for the entire network by up to 23.9% compared to traditional ping-pong buffering. For higher resolution de-noising networks, we achieve activation memory savings of 48.8%. Additionally, we implement a face detector network on an FPGA-based camera to validate these memory savings on a complete end-to-end system.