Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces L^Φ,κ(G) under conditions on Φ 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 Φ(x, t) = t^p(x) + a(x)t^q(x), where p(·) and q(·) satisfy log-Hölder conditions and a(·) is nonnegative, bounded and Hölder continuous.

中文翻译：

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具有可变指数的双相泛函的Trudinger不等式

我们在本文中目的是建立Trudinger对的Musielak-期Orlicz-Morrey空间不等式大号^Φ，κ（ģ上Φ的是基本上比那些在一个前纸视为弱的条件下）。作为一个应用和示例，我们证明了双相函数Φ（x，t）= t ^p（x） + a（x）t ^q（x）的Trudinger不等式，其中p（·）和q（·）满足对数-赫尔德条件和一（·）是非负，有界和Holder连续的。