Works that are in the public domain are those whose intellectual property rights have expired, allowing them to be used freely by the public. In the United States, works published before January 1, 1926, are generally considered public domain.
In the case of Coleman Hawkins, some of his recordings from the early part of his career, when he was with the Fletcher Henderson Orchestra and before he went solo, may fall into the public domain as they might have been recorded before January 1, 1926. However, to confirm if a specific recording is in the public domain, it's best to consult the copyright information provided with the recording or from the relevant copyright holders.