Shaoyu Dai

activity

20132021

collaborators

6 papers

math.AP2021

$L^{2}$ estimate for polynomials of the Laplace operator with Gaussian measure

Shaoyu Dai, Yang Liu, Yifei Pan

Let $P (Δ)$ be a polynomial of the Laplace operator $Δ = \sum_{j = 1}^{n} \frac{\partial ^{2}}{\partial x _{j}^{2}}$ on $R^{n}$ . We prove the existence of weak solutions of the equation $P(…

math.CV2020

$L^{2}$ estimates of Poincaré-Lelong equations on convex domains in $C^{n}$

Shaoyu Dai, Yang Liu, Yifei Pan

In this paper, we prove the existence of solutions of the Poincaré-Lelong equation $- 1 \partial \partial ˉ u = f$ on a strictly convex bounded domain $Ω \subset C^{n}$ $…

math.CV2019

On the Poincare-Lelong equation in $C^{n}$

Shaoyu Dai, Yifei Pan

In this paper, we prove the existence of (global) solutions of the Poincaré-Lelong equation $\partial\overline{\p}u=f$, where $f$ is a $d$ -closed $(1, 1)$ form and is in the weighte…

math.AP2019

A right inverse of differential operator $Δ + a$ in weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$

Shaoyu Dai, Yang Liu, Yifei Pan

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$ .

math.CV2019

A right inverse of Cauchy-Riemann operator $\partial ˉ^{k} + a$ in weighted Hilbert space $L^{2} (C, e^{- ∣ z ∣^{2}})$

Shaoyu Dai, Yifei Pan

Using Hörmander $L^{2}$ method for Cauchy-Riemann equations from complex analysis, we study a simple differential operator $\partial ˉ^{k} + a$ of any order (densely defined and clos…

math.CV2013

A Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces

Shaoyu Dai, Yifei Pan

In this paper we prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, our result says that under a harmonic mapping betwee…

L2 estimate for polynomials of the Laplace operator with Gaussian measure

L2 estimates of Poincaré-Lelong equations on convex domains in Cn

On the Poincare-Lelong equation in Cn

A right inverse of differential operator Δ+a in weighted Hilbert space L2(Rn,e−∣x∣2)

A right inverse of Cauchy-Riemann operator ∂ˉk+a in weighted Hilbert space L2(C,e−∣z∣2)

A Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces

$L^{2}$ estimate for polynomials of the Laplace operator with Gaussian measure

$L^{2}$ estimates of Poincaré-Lelong equations on convex domains in $C^{n}$

On the Poincare-Lelong equation in $C^{n}$

A right inverse of differential operator $Δ + a$ in weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$

A right inverse of Cauchy-Riemann operator $\partial ˉ^{k} + a$ in weighted Hilbert space $L^{2} (C, e^{- ∣ z ∣^{2}})$