SAN FRANCISCO — A federal judge refused on Thursday to allow plaintiffs who claim Apple Inc. double-charged them for music, videos and other digital goods to move forward as a class.

In a 32-page order, U.S. District Judge Lucy Koh of San Jose rejected plaintiffs’ request to certify three classes of customers who claim the Cupertino-based company billed them twice for items they purchased in the iTunes Store, the App Store and the iBookstore. Plaintiffs firms including Berman DeValerio and Pomerantz Grossman Hufford Dahlstrom & Gross sought to certify two classes for damages and another for injunctive relief.