Shuanglin Shao

activity

20072025

most citedMaximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation

22 citations · 124 across the 23 of their papers we have counts for

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8 papers · 1 filter

math.CA2025

Conditional existence of maximizers for the Tomas-Stein inequality for the sphere

Shuanglin Shao, Ming Wang

The Tomas-Stein inequality for a compact subset $Γ$ of the sphere $S^{d}$ states that the mapping $f \mapsto f σ$ is bounded from $L^{2} (Γ, σ)$ to $L^{2 + 4/ d} (R^{d + 1})$ . Then co…

math.CA2015★ 1 cited

On existence of extremizers for the Tomas-Stein inequality for $S^{1}$

Shuanglin Shao

The Tomas-Stein inequality or the adjoint Fourier restriction inequality for the sphere $S^{1}$ states that the mapping $f \mapsto f σ^$ is bounded from $L^{2} (S^{1})$ to $L^6(\mathbb…

math.CA2012

Pointwise convergence of the Schrödinger maximal operator

Shuanglin Shao

This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.

math.CA2010★ 21 cited

Existence of Extremals for a Fourier Restriction Inequality

Michael Christ, Shuanglin Shao

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f \mapsto f σ$ is bounded from $< (S^{2})$ to $L^{4} (R^{3})$ . We prove that there exi…

math.CA2010★ 10 cited

On the extremizers of an adjoint Fourier restriction inequality

Michael Christ, Shuanglin Shao

The adjoint Fourier restriction inequality for the sphere $S^{2}$ states that if $f \in< (S^{2}, σ)$ then $f σ \in L^{4} (R^{3})$ . We prove that all critical points $f$ of the f…

math.CA2010★ 2 cited

On localization of the Schrödinger maximal operator

Shuanglin Shao

In \cite{Lee:2006:schrod-converg}, when the spatial variable $x$ is localized, Lee observed that the Schrödinger maximal operator $e^{i t Δ} f (x)$ enjoys certain localization property…

math.CA2007

A note on the cone restriction conjecture in the cylindrically symmetric case

Shuanglin Shao

In this note, we present two arguments showing that the classical \textit{linear adjoint cone restriction conjecture} holds for the class of functions supported on the cone and inv…

math.CA2007★ 6 cited

Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case

Shuanglin Shao

For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we firs…

Conditional existence of maximizers for the Tomas-Stein inequality for the sphere

On existence of extremizers for the Tomas-Stein inequality for S1

Pointwise convergence of the Schrödinger maximal operator

Existence of Extremals for a Fourier Restriction Inequality

On the extremizers of an adjoint Fourier restriction inequality

On localization of the Schrödinger maximal operator

A note on the cone restriction conjecture in the cylindrically symmetric case

Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case

On existence of extremizers for the Tomas-Stein inequality for $S^{1}$