Anh Nguyen Dao, Nguyen Lam, Guozhen Lu Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-L ∞ spaces Proceedings of the American Mathematical Society DOI: 10.1090/proc/15691 Accepted Manuscript This is a preliminary PDF of the author-produced manuscript that has been peer-reviewed and accepted for publication. It has not been copyedited, proofread, or finalized by AMS Production staff. Once the accepted manuscript has been copyedited, proofread, and finalized by AMS Production staff, the article will be published in electronic form as a “Recently Published Article” before being placed in an issue. That electronically published article will become the Version of Record. This preliminary version is available to AMS members prior to publication of the Version of Record, and in limited cases it is also made accessible to everyone one year after the publication date of the Version of Record. The Version of Record is accessible to everyone five years after publication in an issue.