35 citations · 210 across the 41 of their papers we have counts for
9 papers · 1 filter
The circular maximal operator on Heisenberg radial functions
David Beltran, Shaoming Guo, Jonathan Hickman +1
Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group restricted to a class of Heisenberg radial functions. Under this assu…
Decoupling for two quadratic forms in three variables: a complete characterization
Shaoming Guo, Changkeun Oh, Joris Roos +2
We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in given by two quadratic forms in three variables. Together with previous work…
On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets
Shaoming Guo, Tian Lan, Yakun Xi
We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures.
Reversing a philosophy: from counting to square functions and decoupling
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2
Breakthrough work of Bourgain, Demeter, and Guth recently established that decoupling inequalities can prove powerful results on counting integral solutions to systems of Diophanti…
A bilinear proof of decoupling for the cubic moment curve
Shaoming Guo, Zane Kun Li, Po-Lam Yung
Using a bilinear method that is inspired by the method of efficient congruencing of Wooley [Woo16], we prove a sharp decoupling inequality for the moment curve in .
Maximal functions associated with families of homogeneous curves: bounds for
Shaoming Guo, Joris Roos, Andreas Seeger +1
Let , be the maximal operator and Hilbert transform along the parabola . For we consider estimates for the maximal functio…
Polynomial Roth theorems on sets of fractional dimensions
Robert Fraser, Shaoming Guo, Malabika Pramanik
Let be a closed set of Hausdorff dimension . Let be a polynomial without a constant term whose degree is bigger tha…
Decoupling for certain quadratic surfaces of low co-dimensions
Shaoming Guo, Pavel Zorin-Kranich
We prove sharp decoupling inequalities for quadratic forms in variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:…
A maximal function for families of Hilbert transforms along homogeneous curves
Shaoming Guo, Joris Roos, Andreas Seeger +1
Let be the Hilbert transform along the parabola where . For a set of positive numbers consider the maximal function $\mathcal{H}^U \!f= \s…