In this paper, using the method of blow-up analysis, we obtained a Trudinger-Moser inequality involving L p -norm on a closed Riemann surface and proved the existence of an extremal function for the corresponding Trudinger-Moser functional. This extends an early result of Yang [27]. Similar result in the Euclidean space was also established by Lu-Yang [17].

中文翻译：

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一个 Trudinger-Moser 不等式在闭合黎曼曲面上涉及 Lp 范数

在本文中，我们利用爆破分析的方法，在封闭的黎曼曲面上得到了一个涉及 L p -范数的 Trudinger-Moser 不等式，并证明了对应的 Trudinger-Moser 泛函的极值函数的存在性。这扩展了 Yang [27] 的早期结果。Lu-Yang [17] 在欧几里得空间中也建立了类似的结果。