Shiliang Zhao

activity

20192026

most citedDispersive estimates for time and space fractional Schrödinger equations

1 citations · 2 across the 5 of their papers we have counts for

collaborators

8 papers

math.FA2026

Extension of Sobolev functions on balls in infinite dimensions

Zhouzhe Wang, Xu Zhang, Shiliang Zhao

We prove the existence of a bounded Sobolev extension operator $E : W^{p, 1} (B, P) \to W^{p, 1} (ℓ^{2}, P)$ using a completely new method, where $B\s…

math.FA2026

" $H = W$ " in infinite dimensions

Zhouzhe Wang, Jiayang Yu, Xu Zhang +1

The classical `` $H = W$ " theorem establishes the identity between two function spaces on an arbitrary nonempty open set in the Euclidean spaces: the space $W$ defined via weak deriva…

math.CA2020

Uniform Complex Time Heat Kernel Estimates Without Gaussian Bounds

Shiliang Zhao, Quan Zheng

In this paper, first we consider the uniform complex time heat kernel estimates of $e^{- z (- Δ)^{\frac{α}{2}}}$ for $α > 0, z \in C^{+}$ . When $\frac{α}{2}$ is not an integer, genera…

math.DG2020

Conformal Perturbation of Heat Kernels with applications

Shiliang Zhao

Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n \geq 2$ . Consider the conformal perturbation $g ~ = h g$ where $h$ is a smooth bounded positive function on $M$ .…

math.AP2019

Global well-posedness of cubic fractional Schrödinger equations in one dimension

Huali Zhang, Shiliang Zhao

In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schrödinger equations in o…