According to the eighteenth page of the Compendium of U.S. Copyright Office Practices' 2,200th chapter, a book's dust jacket requires a separate copyright from the book that it is attached to:

"A notice of copyright on the dust jacket of a book is not an acceptable notice for the book, because the dust jacket is not permanently attached to the book. Likewise, a notice appearing in a book is not an acceptable notice for the dust jacket or any material appearing on that dust jacket, even if the book refers to the jacket or material appearing on the jacket."