Shaoming Guo

activity

20142026

most citedMaximal operators and Hilbert transforms along variable non-flat homogeneous curves

35 citations · 210 across the 41 of their papers we have counts for

collaborators

Showing 2016Show all

8 papers · 1 filter

math.CA2016

Single annulus estimates for the variation-norm Hilbert transforms along Lipschitz vector fields

Shaoming Guo

Let v be a planar Lipschitz vector field. We prove that the r-th variation-norm Hilbert transform along v, composed with a standard Littlewood-Paley projection operator P_k, is bou…

math.CA2016★ 35 cited

Maximal operators and Hilbert transforms along variable non-flat homogeneous curves

Shaoming Guo, Jonathan Hickman, Victor Lie +1

We prove that the maximal operator associated with variable homogeneous planar curves $(t, u t^{α})_{t \in R}$ , $α \neq = 1$ positive, is bounded on $L^{p} (R^{2})$ for each…

math.CA2016★ 2 cited

Sharp decouplings for three dimensional manifolds in $R^{5}$

Ciprian Demeter, Shaoming Guo, Fangye Shi

We prove a sharp decoupling for a class of three dimensional manifolds in $R^{5}$ .

math.CA2016★ 14 cited

Schrödinger maximal function estimates via the pseudoconformal transformation

Ciprian Demeter, Shaoming Guo

We present an alternative way to recover the recent result from \cite{LR} using the pseudoconformal transformation.

math.NT2016★ 3 cited

Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions

Jean Bourgain, Ciprian Demeter, Shaoming Guo

We prove a sharp decoupling for a certain two dimensional surface in R^9. As an application, we obtain the full range of expected estimates for the cubic Parsell-Vinogradov system…

math.AP2016★ 3 cited

Local Well-Posedness for the Derivative Nonlinear Schrödinger Equations with $L^{2}$ Subcritical Data

Shaoming Guo, Xianfeng Ren, Baoxiang Wang

We will show its local well-posedness in modulation spaces $M^{1/2}_{2,q}({\Real})$ $(2 \leq q < \infty)$ . It is well-known that $H^{1/2}$ is a critical Sobolev space of DNLS so that…

math.CA2016★ 1 cited

Hilbert transforms along Lipschitz direction fields: A lacunary model

Shaoming Guo, Christoph Thiele

We prove bounds for the truncated directional Hilbert transform in $L^{p} (R^{2})$ for any $1 < p < \infty$ under a combination of a Lipschitz assumption and a lacunarity assumptio…

math.CA2016★ 3 cited

Remarks on Wolff's inequality for hypersurfaces

Shaoming Guo, Changkeun Oh

We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$ -cones. These are extensions of results…