Mathematical Inequalities & Applications · Volume 23, Issue 1 Sobolev's theorem for double phase functionals 23-02 Pages 17-33 DOI 10.7153/mia-2020-23-02 Downloads Short PDF Full PDF PNG Authors Yoshihiro Mizuta Takao Ohno Tetsu Shimomura Keywords Sobolev's embedding theorem fractional maximal functions maximal functions Sobolev's theorem Musielak-Orlicz spaces double phase functionals continuity Subject classes 46E30 42B25 46E35