which application domains are not well suited to deep learning?
Deep learning is generally not well suited for domains that have only very small training datasets. This includes fields like medicine where, for example, patient data can only be obtained through expensive and time consuming clinical trials. Clinical trials will often contain only several hundreds records. 

By design, deep learning models have many parameters (e.g., millions), and like with any machine learning algorithm, you're likely to see overfitting when the number of parameters greatly exceeds the number of training records.