Dr Trang Nguyen
T: +61 3 99054500
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.
 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.
 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.