Michael Mitchell; the credit "Jacket design by Michael Mitchell" is found on the right jacket flap (the left panel). (For jurisdictions that do not recognize the rule of the shorter term, and define copyright term based the date of the author's death plus a set number of years: according to this post at Cal Arts, Mitchell died in 2009.)
First, the photo is a mechanical scan/photocopy of the original cover and does not qualify for independent copyright protection.
Second, the dust jacket was first published prior to 1978 without a valid copyright notice. The Catcher in the Rye was first published in 1951; the hardcover book itself carried a copyright notice, so its contents remain copyrighted. However, the first-edition dust jacket did not carry a separate copyright notice. According to The Compendium of U.S. Copyright Office Practices: Chapter 2200, § 2207.1(C) at p. 15:
"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."
The jacket's lack of a copyright notice can be verified from the full scan, linked below.
Keep in mind that the pre-1989 requirements for copyright notice were highly formalistic and, other than a few enumerated exceptions, required these three elements:
"The name of the copyright owner, or an abbreviation by which the name can be recognized, or a generally known alternative designation of the owner."
If just one of these elements is omitted, the work is deemed to be published without notice and is not eligible for copyright protection. Neither the year "1951" nor a copyright symbol (or any acceptable variant) appear anywhere on the dust jacket. Credits like "Jacket design by Michael Mitchell" do not meet these requirements, nor do the identifications of the publisher and author.
This image is in the public domain because it is a mere mechanical scan or photocopy of a public domain original, or – from the available evidence – is so similar to such a scan or photocopy that no copyright protection can be expected to arise. The original itself is in the public domain for the following reason:
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (50 p.m.a.), Mainland China (50 p.m.a., not Hong Kong or Macao), Germany (70 p.m.a.), Mexico (100 p.m.a.), Switzerland (70 p.m.a.), and other countries with individual treaties.
This tag is designed for use where there may be a need to assert that any enhancements (eg brightness, contrast, colour-matching, sharpening) are in themselves insufficiently creative to generate a new copyright. It can be used where it is unknown whether any enhancements have been made, as well as when the enhancements are clear but insufficient. For known raw unenhanced scans you can use an appropriate {{PD-old}} tag instead. For usage, see Commons:When to use the PD-scan tag.
Note: This tag applies to scans and photocopies only. For photographs of public domain originals taken from afar, {{PD-Art}} may be applicable. See Commons:When to use the PD-Art tag.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse
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First-edition cover of The Catcher in the Rye(1951)
{{Information |Description=First-edition cover of ''The Catcher in the Rye'' (1951) by the American author J. D. Salinger. |Source=[https://natedsanders.com/lot-30795.aspx Nate D. Sanders auctions] ([https://natedsanders.com/ItemImages/000030/43592i_lg.jpeg direct link to jpg]). Retouched by uploader. |Date=1951 |Author=Michael Mitchell; the credit "Jacket design by Michael Mitchell" is found on the right jacket flap...