Received November 28, 2019. Published online January 25, 2021.
Abstract: Our aim in this paper is to establish Trudinger's inequality on Musielak-Orlicz-Morrey spaces $L^{\Phi,\kappa}(G)$ under conditions on $\Phi$ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger's inequality for double phase functionals $\Phi(x,t) = t^{p(x)} + a(x) t^{q(x)}$, where $p(\cdot)$ and $q(\cdot)$ satisfy log-Hölder conditions and $a(\cdot)$ is nonnegative, bounded and Hölder continuous.
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Affiliations: Fumi-Yuki Maeda, 4-24 Furue-higashi-machi, Nishi-ku, Hiroshima 733-0872, Japan, e-mail: fymaeda@h6.dion.ne.jp; Yoshihiro Mizuta, Department of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8521, Japan, e-mail: yomizuta@hiroshima-u.ac.jp; Takao Ohno (corresponding author), Faculty of Education, Oita University, Dannoharu Oita-city 870-1192, Japan, e-mail: t-ohno@oita-u.ac.jp, Tetsu Shimomura, Department of Mathematics, Graduate School of Humanities and Social Sciences, Hiroshima University, Higashi-Hiroshima 739-8524, Japan, e-mail: tshimo@hiroshima-u.ac.jp
