Geodesic
Trudinger's inequality for double phase functionals with variable exponents
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 511-528.

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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.
DOI : 10.21136/CMJ.2021.0506-19
Classification : 31C15, 46E30
Keywords: Riesz potential; Trudinger's inequality; Musielak-Orlicz-Morrey space; double phase functional 
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     title = {Trudinger's inequality for double phase functionals with variable exponents},
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Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu. Trudinger's inequality for double phase functionals with variable exponents. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 511-528. doi : 10.21136/CMJ.2021.0506-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0506-19/

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