Dr Trang Nguyen

 

T: +61 3 99054500
E: Trang.TT.Nguyen@monash.edu

Research Overview

My primary research interests lie in the areas of functional analysis, harmonic analysis and their applications on PDEs. I focus on the study of functional inequalities (e.g. Poincaré inequality, reverse Holder inequality, Muckenhoupt Ap inequality), the singular integral operators developed by Calderon and Zygmund (e.g. Hilbert transform, Cauchy integral); different classes of functions (e.g. BMO, VMO, quasiconformal maps, Lp spaces); and the underlying spaces on which the functions act (e.g. Euclidean spaces, metric measure spaces, spaces of homogeneous type). Currently, I am developing harmonic analysis tools which help us understand the solutions to the nonlinear PDEs of dispersive types, such as Schrodinger equation, KdV equations.

Selected Publications

[1] Functions of bounded mean oscillation and quasiconformal mappings on spaces of homogeneous type, with: L.A. Ward, The Journal of Geometric Analysis, Vol. 31, no. 12, 2021, 12182–12230.

[2] The Cauchy integral, bounded and compact commutators, with: J. Li, L.A. Ward, B.D. Wick, Studia Mathematica, Vol. 250, no. 2, 2020, 193--216.