# Publications

Preprints

1. Dimensional variance inequalities on Riemannian manifolds with boundary, In preparation.
2. Sharp Sobolev inequality on the Heisenberg type groups, In preparation.
3. Sharp Gagliardo-Nirenberg trace inequalities via mass transport and their affine versions, preprint. (pdf)
4. The sharp Gagliardo-Nirenberg-Sobolev inequality in quantitative form, preprint. (arXiv link)
5. Stability results for Gagliardo-Nirenberg-Sobolev inequality via mass transport, In preparation.
6. Valuations on Sobolev space $W^{1,p}(\mathbb{R}^n), p > 1$, work in progress.
7. Sobolev trace inequalities for derivatives of higher order. In preparation.
8. An improvement for the sharp Adams  inequalities in bounded domains and whole space $\mathbb{R}^n$, preprint. (arXiv link)
9. Sharp Adams-Moser-Trudinger type inequalities in the hyperbolic space, submitted. (with Quoc Anh Ngo) (arXiv link)
10. Sharp constant for Poincaré-type inequalities in the hyperbolic space, submitted. (with Quoc Anh Ngo) (arXiv link)
11. Orlicz-Lorentz centroid bodies, submitted. (arXiv link)
12. Remark on Hardy-Rellich type inequality, preprint. (pdf)
13. A sharp Adams inequality in dimension four and its extremal functions, submitted. (arXiv link)
14. Extremal functions for the Moser-Trudinger inequality of Adimurthi-Druet type in $W^{1,N}(\mathbb R^N)$, submitted. (arXiv link)
15. Improved Moser-Trudinger inequality for functions with mean value zero in $\mathbb R^n$ and its extremal functions, preprint.
16. An improved Moser-Trudinger inequality involving the first non-zero Neumann eigenvalue with mean value zero in $\mathbb R^2$, preprint. (with Quoc Anh Ngo) (arXiv link)
17. On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem, submitted. (with Futoshi Takahashi) (pdf) (arXiv link)
18. A pointwise inequality for a biharmonic equation with negative exponent and related problems, submitted. (arXiv link) (with Quoc Anh Ngo and Quoc Hung Phan)
19. Extremal functions for the sharp Moser-Trudinger type inequalities in whole space $\mathbb R^N$, submitted. (arXiv link)
20. Existence of maximizers for the critical sharp Moser-Trudinger inequality in $\mathbb R^N$ under constraints, submitted.
21. Maximizers for the variational problems associated with Sobolev type inequalities under constraints, preprint. (arXiv link)

Publications

1. Ha Huy Bang, Nguyen Van Hoang, and Vu Nhat Huy, Best constants for the inequalities between equivalent norms in Orlicz spaces, Bull. Poli. Acad. Sci. Math, 59 (2) (2011) 165-174.(pdf) (link)
2. Ha Huy Bang, Nguyen Van Hoang, and Vu Nhat Huy, Some properties of Orlicz-Lorentz spaces, Acta Math. Vietnam, 36 (2) (2011) 145-169. (pdf) (link)
3. Keith Ball, and Van Hoang Nguyen, Entropy jumps for log-concave isotropic random vectors and spectral gap, Studia Math. 213 (1) (2012) 81-96. (pdf) (link)
4. Van Hoang Nguyen, Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prekopa’s theorem, J. Funct. Anal. 266 (2014), 931-955. (pdf) (link)
5. Van Hoang Nguyen, A local proof of the dimensional Prékopa’s theorem, J. Math. Anal. Appl. 419 (2014) 20-27. (pdf) (link)
6. Van Hoang Nguyen, Sharp weighted Sobolev and Gagliardo-Nirenberg inequalities on half spaces via mass transport and consequences, Proc. London Math. Soc. 111 (2015) 127-148. (arXiv link) (link)(pdf)
7. Van Hoang Nguyen, Improved $L_p-$mixed volume inequality for convex bodies, J. Math. Anal. Appl. 431 (2015) 1045-1053. (pdf) (link)
8. Van Hoang Nguyen, Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz’ya type inequalities, J. Funct. Anal.,  270 (2016), 4117-4151.  (arXiv link) (link)(pdf)
9. Van Hoang Nguyen, New approach to the affine Polya-Szego principle and the stability version of the affine Sobolev inequality, Adv. Math., 302 (2016), 1080-1110. (arXiv link) (link)
10. Quoc Anh Ngo, and Van Hoang Nguyen, Sharp reversed Hardy-Littlewood-Sobolev inequality on the half space $\mathbb{R}^n_+$, to appear in International Mathematics Research Notices. (arXiv link) (link)
11. Quoc Anh Ngo, and Van Hoang Nguyen, Sharp reversed Hardy-Littlewood-Sobolev inequality on  $\mathbb{R}^n$to appear in Israel Journal of Mathematics. (link)
12. Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities, revision in Adv. Differential Equations. (with G. Jankowiak) (arXiv link)

My PhD thesis

Inégalités fonctionnelles et convexité” sous la direction de Prof. Dario Cordero-Erausquin (UPMC). (pdf)

Jury: F. Barthe (Rapporteur), M. Fradelizi, I. Gentil, N. Gigli and B. Klartag (Rapporteur).