Cross-corpus speech emotion recognition (SER) poses a challenge due to feature distribution mismatch, potentially degrading the performance of established SER methods. In this paper, we tackle this challenge by proposing a novel transfer subspace learning method called acoustic knowledgeguided transfer linear regression (AKTLR). Unlike existing approaches, which often overlook domain-specific knowledge related to SER and simply treat cross-corpus SER as a generic transfer learning task, our AKTLR method is built upon a well-designed acoustic knowledge-guided dual sparsity constraint mechanism. This mechanism emphasizes the potential of minimalistic acoustic parameter feature sets to alleviate classifier overadaptation, which is empirically validated acoustic knowledge in SER, enabling superior generalization in cross-corpus SER tasks compared to using large feature sets. Through this mechanism, we extend a simple transfer linear regression model to AKTLR. This extension harnesses its full capability to seek emotiondiscriminative and corpus-invariant features from established acoustic parameter feature sets used for describing speech signals across two scales: contributive acoustic parameter groups and constituent elements within each contributive group. Our proposed method is evaluated through extensive cross-corpus SER experiments on three widely-used speech emotion corpora: EmoDB, eNTERFACE, and CASIA. The results confirm the effectiveness and superior performance of our method, outperforming recent state-of-the-art transfer subspace learning and deep transfer learning-based cross-corpus SER methods. Furthermore, our work provides experimental evidence supporting the feasibility and superiority of incorporating domain-specific knowledge into the transfer learning model to address cross-corpus SER tasks.