Introduced as an extension of the Cloud at the network edge for computing and storage purposes, the Fog is increasingly considered a key enabler for Internet-of-Things applications whose latency requirements are not compatible with a Cloud-only approach. Unlike Cloud platforms, which can elastically accommodate large numbers of requests, Fog deployments are usually dimensioned for an average traffic load and, thus, unable to handle sudden bursts of requests without violating latency guarantees. In this article, we address the problem of efficiently controlling Fog admission to guarantee application response time. We propose request-aware admission control (AC) strategies maximizing the number of Fog-handled requests by means of dynamic popularity estimation. In particular, the LRU-AC, an AC strategy based on online learning of the request popularity distribution via a Least Recently Used (LRU) filter, is introduced. We contribute an analytical model for assessing LRU-AC performance and quantifying the incurred reduction of Cloud offload cost, w.r.t. both an ideal oracle-based and a request-oblivious AC strategy. Further, we propose a feasible implementation design of LRU-AC on FPGA hardware using Aging Bloom Filters (ABF) to mimic the function of the LRU-AC, while providing a compact memory representation. The use of ABFs for LRU-AC is theoretically validated and verified through simulation. The current implementation shows a throughput of 16.7 Mpps and a processing latency of less than 3μ s while multiplying the Fog acceptance-rate by 10 in the evaluated scenario.