Reseach Interests
Harmonic Analysis
Functional and Geometric Inequalities
Geometric Analysis
Partial Differential Equations
Publications
Sharp stability of the Heisenberg Uncertainty Principle: Second-order and curl-free field cases, (A.X. Do, N. Lam, G. Lu), Journal of Functional Analysis, 2026.
Sobolev interpolation inequalities with optimal Hardy-Rellich inequalities and critical exponents, (N.A. Dao, A.X. Do, N. Lam, G. Lu), Calculus of Variations and Partial Differential Equations, 2025.
Some analytic and geometric aspects of weighted p-Laplacian on smooth metric measure spaces, (H.T. Dung, A.X. Do, N.T. Dung), International Journal of Mathematics, 2025.
A New Approach to Weighted Hardy-Rellich Inequalities: Improvements, Symmetrization Principle and Symmetry Breaking, (A.X. Do, N. Lam, G. Lu), The Journal of Geometric Analysis, 2024.
Hardy Type Identities on R^{n-k} x (R+)^k via Factorizations, (N.A. Dao, A.X. Do, N.T. Duy, N. Lam), Vietnam Journal of Mathematics, 2023.
Preprints
Optimal AB-program for Poincar\'e--Sobolev and logarithmic Sobolev inequalities on hyperbolic spaces, (A.X. Do, D. Ganguly, N. Lam, G. Lu), arXiv:2611.01161.
Second order Heisenberg Uncertainty Principle for solenoidal fields: sharp constants, optimizers and sharp stability, (A.X. Do, A.T. Duong, N. Lam, V.H. Nguyen, G. Lu), arXiv:2611.00362.
A Fourier approach to the sharp stability of Heisenberg Uncertainty Principles of higher and fractional orders: a new perspective, (A.X. Do, N. Lam, V.H. Nguyen, G. Lu), arXiv:2609.31949.
Optimal stability hierarchies of the Heisenberg Uncertainty Principle for solenoidal fields and of the second order Caffarelli--Kohn--Nirenberg inequalities, (A.X. Do, A.T. Duong, N. Lam, V.H. Nguyen, G. Lu), arXiv:2609.31579.
Polya-Szego Inequality on Submanifolds of Riemannian Manifolds with Nonnegative Curvature and Applications, (A.X. Do, N. Lam, G. Lu, R. Ponciano), arXiv:2609.22676.
Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp L^2 stability and L^p extensions, (A.X. Do, N. Lam, G. Lu, V.H. Nguyen), arXiv:2606.08939.
Logarithmic Sobolev, Poincaré and Beckner Inequalities on Hyperbolic Spaces and Riemannian Manifolds, (A.X. Do, D. Ganguly, N. Lam, G. Lu), arXiv:2602.14202.
Scale-Dependent Poincaré inequalities and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space, (A.X. Do, D. Ganguly, N. Lam, G. Lu), arXiv:2410.21039.
L^p-Caffarelli-Kohn-Nirenberg inequalities and their stabilities, (A.X. Do, J. Flynn, N. Lam, G. Lu), arXiv:2310.07083.