Top-$k$ frequent items detection is a fundamental task in data stream mining. Many promising solutions are proposed to improve memory efficiency while still maintaining high accuracy for detecting the Top-$k$ items. Despite the memory efficiency concern, the users could suffer from privacy loss if participating in the task without proper protection, since their contributed local data streams may continually leak sensitive individual information. However, most existing works solely focus on addressing either the memory-efficiency problem or the privacy concerns but seldom jointly, which cannot achieve a satisfactory tradeoff between memory efficiency, privacy protection, and detection accuracy. In this paper, we present a novel framework HG-LDP to achieve accurate Top-$k$ item detection at bounded memory expense, while providing rigorous local differential privacy (LDP) protection. Specifically, we identify two key challenges naturally arising in the task, which reveal that directly applying existing LDP techniques will lead to an inferior ``accuracy-privacy-memory efficiency'' tradeoff. Therefore, we instantiate three advanced schemes under the framework by designing novel LDP randomization methods, which address the hurdles caused by the large size of the item domain and by the limited space of the memory. We conduct comprehensive experiments on both synthetic and real-world datasets to show that the proposed advanced schemes achieve a superior ``accuracy-privacy-memory efficiency'' tradeoff, saving $2300\times$ memory over baseline methods when the item domain size is $41,270$. Our code is open-sourced via the link.