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In their celebrated work [5], Chang and Marshall established a critical traceinequality of Moser-Trudinger type for holomorphic functions with mean valuezero on unit disc in the complex plane. The main purpose is to address aquestion proposed to us by S. Y. Alice Chang who asked whether theChang-Marshall type inequality for holomorphic functions on unit disk in thecomplex plane holds for Sobolev functions on general domains in higherdimensional Euclidean space $\mathbb{R}^n$ for all $n\ge 2$. We partiallyanswer her question affirmatively.

The Chang-Marshall Trace Inequality for Sobolev functions in domains in higher dimensional space $\mathbb{R}^n$