12 papers · 1 filter
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…
Sobolev improving for averages over curves in
David Beltran, Shaoming Guo, Jonathan Hickman +1
We study -Sobolev improving for averaging operators given by convolution with a compactly supported smooth density on a non-degenerate curve. In particular, in 4 d…
A variable coefficient multi-frequency lemma
Shaoming Guo, Pavel Zorin-Kranich
We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by K…
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…
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.