双曲空间中的Moser-Trudinger不等式
Moser-Trudinger Inequalities in Hyperbolic Spaces
摘要: 本文利用分割水平集的技巧，借助于非增重排理论和O’Neil’s引理，把Moser-Trudinger不等式推广到双曲空间，所得结果推广和改进了近期的相应结果。
Abstract: In this paper, the Moser-Trudinger inequality is extended to hyperbolic space by using the technique of level set segmentation, non increasing rearrangement theory and O’Neil’s lemma. The results generalize and improve the recent results.
文章引用：郭明娟, 王广兰. 双曲空间中的Moser-Trudinger不等式[J]. 应用数学进展, 2021, 10(2): 453-460. https://doi.org/10.12677/AAM.2021.102051

参考文献

[1] Wolf, J. (1967) Space of Constant Curvature. McGraw-Hill, New York.
[2] Lam, N. and Lu, G. (2013) A New Approach to Sharp Moser-Trudinger and Adams Type Inequalities: A Rearrangement-Free Argument. Journal of Differential Equations, 255, 298-325. [Google Scholar] [CrossRef] 
[3] Lam, N. and Lu, G. (2012) Sharp Moser-Trudinger Inequality in the Heisenberg Group at the Critical Case and Applications. Advances in Mathematics, 231, 3259-3287. [Google Scholar] [CrossRef] 
[4] Lam, N., Lu, G. and Tang, H. (2017) Sharp Affine and Improved Moser-Trudinger-Adams Type Inequalities on Unbounded Domains in the Spirit of Lions. Journal of Geometric Analysis, 27, 300-334. [Google Scholar] [CrossRef] 
[5] Lam, N., Lu, G. and Tang, H. (2014) Sharp Subcritical Moser-Trudinger Inequalities on Heisenberg Groups and Subelliptic PDEs. Nonlinear Analysis, 95, 77-92. [Google Scholar] [CrossRef] 
[6] Lam, N., Lu, G. and Zhang, L. (2017) Equivalence of Critical and Subcritical Sharp Trudinger-Moser-Adams Inequalities. Revista Matemática Iberoamericana, 33, 1219-1246. [Google Scholar] [CrossRef] 
[7] Lu, G. and Yang, Q. (2017) Sharp Hardy-Adams Inequalities for Bi-Laplacian on Hyperbolic Space of Dimension Four. Advances in Mathematics, 319, 567-598. [Google Scholar] [CrossRef] 
[8] Li, J.G., Lu, G. and Yang, Q. (2018) Fourier Analysis and Optimal Hardy-Adams Inequalities on Hyperbolic Spaces of Any Even Dimension. Advances in Mathematics, 333, 350-385.
[9] O’Neil, R. (1963) Convolution Operators and L(p,q) Spaces. Duke Mathematical Journal, 30, 129-142. [Google Scholar] [CrossRef] 
[10] Adams, D. (1988) A Sharp Inequality of J. Moser for Higher Order Derivatives. Annals of Mathematics, 128, 385-398. [Google Scholar] [CrossRef] 
[11] Dong, Y. and Yang, Q. (2016) An Interpolation of Hardy Inequality and Moser-Trudinger Inequality on Riemannian Manifolds with Negative Curvature. Acta Mathematica Sinica, English Series, 32, 856-866. [Google Scholar] [CrossRef] 
[12] Nguyen, V.H. (2018) Improved Moser-Trudinger Type Inequalities in the Hyperbolic Space H. Nonlinear Analysis, 168, 67-80. [Google Scholar] [CrossRef] 
[13] Adachi, S. and Tanaka, K. (2000) Trudinger Type Inequalities in {R} N and Their Best Exponents. Proceedings of the American Mathematical Society, 128, 2051-2057. [Google Scholar] [CrossRef] 
[14] Lam, N. and Lu, G. (2015) Sharp Singular Trudinger-Moser-Adams Inequalities with Exact Growth. In: Geometric Methods in PDE’s, Springer, Berlin, 43-80.
[15] Nguyen, V.H. (2019) The Sharp Hardy-Moser-Trudinger Inequality in Dimension N.
[16] Wang, G. and Ye, D. (2012) A Hardy-Moser-Trudinger Inequality. Advances in Mathematics, 230, 294-320. [Google Scholar] [CrossRef] 

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