Khanh Vu Tran

activity

20102026

most citedA general method of weights in the d-bar-Neumann problem

14 citations · 30 across the 15 of their papers we have counts for

collaborators

18 papers

math.CV2026

$L^{p}$ Estimates for the $\partial ˉ$ -Problem on Rational Hartogs Triangles

Tran Vu Khanh, Tu Nguyen

We investigate $L^{p}$ estimates for the $\partial ˉ$ -problem on rational Hartogs triangles $H_{m / n} = {(z_{1}, z_{2}) \in C^{2} : ∣ z_{1} ∣^{m} < ∣ z_{2} ∣^{n} < 1}$ . For $p…

math.CV2019

Bergman-Toeplitz operators between weighted $L^{p}$ -spaces on weakly pseudoconvex domains

Tran Vu Khanh, Pham Trong Tien

In this paper we study the Bergman-Toeplitz operator $T_{ψ}$ induced by $ψ (w) = K_{Ω}^{- α} (w, w) d_{Ω}^{β} (w)$ with $α, β \geq 0$ acting from a weighted $L^{p}$ -space $L_{a}^{p} (Ω)$ to another one…

math.CV2017

Equivalence of estimates on domain and its boundary

Tran Vu Khanh

Let $Ω$ be a pseudoconvex domain in $C^{n}$ with smooth boundary $b Ω$ . We define general estimates $(f - M)_{Ω}^{k}$ and $(f - M)_{b Ω}^{k}$ on $k$ -forms…

math.CV2016

The Kohn-Laplace equation on abstract CR manifolds: Local regularity

Tran Vu Khanh

The purpose of this paper is to establish local regularity of the solution operator to the Kohn-Laplace equation, called the complex Green operator, on abstract CR manifolds of hyp…

math.CV2016

The Kohn-Laplace equation on abstract CR manifolds: Global regularity

Tran Vu Khanh, Andrew Raich

Let $M$ be a compact, pseudoconvex-oriented, $(2 n + 1)$ -dimensional, abstract CR manifold of hypersurface type, $n \geq 2$ . We prove the following: (i) If $M$ admits a strictly CR-plu…

math.CV2015

Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in $C^{n}$

Tran Vu Khanh, Ninh Van Thu

We prove here the Wolff-Denjoy-type theorem for a very large class of pseudoconvex domains in $C^{n}$ that may contain many classes of pseudoconvex domains of finite type and…

math.CV2015★ 1 cited

Hölder regularity of the solution to the complex Monge-Ampère equation with $L^{p}$ density

Luca Baracco, Tran Vu Khanh, Stefano Pinton +1

On a smooth domain $Ω \subset\subset C^{n}$ , we consider the Dirichlet problem for the complex Monge-Ampère equation $((d d^{c} u)^{n} = f d V, u ∣_{b Ω} \equiv ϕ)$ . We state the Hölder reg…

math.CV2014★ 4 cited

Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type

Tran Vu Khanh, Andrew Raich

The purpose of this paper is to prove that if a pseudoconvex domains $Ω \subset C^{n}$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman pro…

math.CV2014

Local regularity of the Green operator in a CR manifold of general "type"

Luca Baracco, Tran Vu Khanh, Stefano Pinton +1

It is here proved that if a pseudoconvex CR manifold $M$ of hypersurface type has a certain "type", that we quantify by a vanishing rate $F$ at a submanifold of CR dimension $0$ , t…

math.CV2014

Boundary regularity of the solution to the Complex Monge-Ampère equation on pseudoconvex domains of infinite type

Ly Kim Ha, Tran Vu Khanh

Let $Ω$ be a bounded, pseudoconvex domain of $C^{n}$ satisfying the " $f$ -Property". The $f$ -Property is a consequence of the geometric "type" of the boundary; it holds for al…

math.CV2013

Lower bound for the geometric type from a generalized estimate in the $\dib$-Neumann problem - a new approach by peak functions

Tran Vu Khanh

We give a simple proof of the fact that an " $f$ -estimate" for the $\partial ˉ$ -Neumann problem implies a lower bound on the geomatric type of the boundary along any complex one d…

math.CV2013★ 3 cited

Boundary behavior of the Kobayashi metric near a point of infinite type

Tran Vu Khanh

Under a potential-theoretical hypothesis named $f$ -Property with $f$ satisfying $\int_{t}^{\infty} \frac{d a}{a f ( a )} < \infty$ , we show that the Kobayashi metric $K (z, X)$ o…

math.CV2012★ 1 cited

Supnorm and f-Holder estimates for di-bar on convex domains of general type in C^2

Tran Vu Khanh

In this paper, we study supnorm and modified Hölder estimates for the integral solution of the di-bar-equation on a class of convex domains of general type in $\C^2$ that includes…

math.CV2010★ 6 cited

Global hypoellipticity of the Kohn-Laplacian $□_{b}$ on pseudoconvex CR manifolds

Tran Vu Khanh

Let $X$ be a complex manifold and $M \subset X$ a compact, smooth, pseudoconvex CR manifold of dimension $2 n - 1$ . (Here $n \geq 3$ or, in case $n = 2$ , it is made the extra assumption th…

math.CV2010

Loss of derivatives in the infinite type

T. V. Khanh, S. Pinton, G. Zampieri

We discuss loss of derivatives for degenerate vector fields obtained from infinite type exponentially non-degenerate hypersurfaces of $\C^2$.

math.CV2010

Loss of derivatives for systems of complex vector fields and sums of squares

Tran Vu Khanh, Stefano Pinton, Giuseppe Zampieri

We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.

math.CV2010★ 1 cited

Hypoellipticity of the $\partial ˉ$ -Neumann problem at exponentially degenerate points

Tran Vu Khanh, Giuseppe Zampieri

We prove that the $\partial ˉ$ -Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR d…

math.CV2010★ 14 cited

A general method of weights in the d-bar-Neumann problem

Tran Vu Khanh

This thesis deals with Partial Differential Equations in Several Complex Variables and especially focuses on a general estimate for the $\partial ˉ$ -Neumann problem on a domain w…

Lp Estimates for the ∂ˉ-Problem on Rational Hartogs Triangles

Bergman-Toeplitz operators between weighted Lp-spaces on weakly pseudoconvex domains

Equivalence of estimates on domain and its boundary

The Kohn-Laplace equation on abstract CR manifolds: Local regularity

The Kohn-Laplace equation on abstract CR manifolds: Global regularity

Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in Cn

Hölder regularity of the solution to the complex Monge-Ampère equation with Lp density

Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type

Local regularity of the Green operator in a CR manifold of general "type"

Boundary regularity of the solution to the Complex Monge-Ampère equation on pseudoconvex domains of infinite type

Lower bound for the geometric type from a generalized estimate in the $\dib$-Neumann problem - a new approach by peak functions

Boundary behavior of the Kobayashi metric near a point of infinite type

Supnorm and f-Holder estimates for di-bar on convex domains of general type in C^2

Global hypoellipticity of the Kohn-Laplacian □b​ on pseudoconvex CR manifolds

Loss of derivatives in the infinite type

Loss of derivatives for systems of complex vector fields and sums of squares

Hypoellipticity of the ∂ˉ-Neumann problem at exponentially degenerate points

A general method of weights in the d-bar-Neumann problem

$L^{p}$ Estimates for the $\partial ˉ$ -Problem on Rational Hartogs Triangles

Bergman-Toeplitz operators between weighted $L^{p}$ -spaces on weakly pseudoconvex domains

Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in $C^{n}$

Hölder regularity of the solution to the complex Monge-Ampère equation with $L^{p}$ density

Global hypoellipticity of the Kohn-Laplacian $□_{b}$ on pseudoconvex CR manifolds

Hypoellipticity of the $\partial ˉ$ -Neumann problem at exponentially degenerate points