22 citations · 28 across the 9 of their papers we have counts for
9 papers
Mixed-norm Brascamp-Lieb inequalities
Ruixiang Zhang
Christ [Chr01] looked at a certain boundedness problem for trilinear operators. In this paper we set up a framework of mixed-norm Brascamp-Lieb inequalities and identify a new inte…
Curved Kakeya problems and the projective geometry of paths
Shaoming Guo, Larry Guth, Arian Nadjimzadah +2
We introduce a general framework for curved Kakeya problems in , encompassing those arising from Hörmander-type oscillatory integrals. Every family of curves determin…
integrability of functions with Fourier support on a smooth space curve
Shaoming Guo, Alex Iosevich, Ruixiang Zhang +1
We prove that if with satisfies that is supported on a small perturbation of the moment curve in , then is…
Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems
Song Dai, Liuwei Gong, Shaoming Guo +1
We consider Carleson-Sjölin operators on Riemannian manifolds that arise naturally from the study of Bochner-Riesz problems on manifolds. They are special cases of Hörmander-type o…
A dichotomy for Hörmander-type oscillatory integral operators
Shaoming Guo, Hong Wang, Ruixiang Zhang
In this paper, we first generalize the work of Bourgain and state a curvature condition for Hörmander-type oscillatory integral operators, which we call Bourgain's condition. This…
The Bochner-Riesz problem: an old approach revisited
Shaoming Guo, Changkeun Oh, Hong Wang +2
We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner-Riesz problem. This is achieved via applying a pseudo-confor…
A stationary set method for estimating oscillatory integrals
Saugata Basu, Shaoming Guo, Ruixiang Zhang +1
We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimen…
Decoupling inequalities for quadratic forms
Shaoming Guo, Changkeun Oh, Ruixiang Zhang +1
We prove sharp decoupling inequalities for and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for qu…
On integer solutions of Parsell-Vinogradov systems
Shaoming Guo, Ruixiang Zhang
We prove a sharp upper bound on the number of integer solutions of the Parsell-Vinogradov system in every dimension .