52 citations · 278 across the 40 of their papers we have counts for
45 papers
Reduction for flag-transitive symmetric 2-designs with gcd(k, λ) = p
Ziwei Lu, Yu Sun, Shenglin Zhou
We study symmetric 2-(v, k, λ) designs admitting a flag-transitive point-primitive subgroup G of automorphisms, where gcd(k, λ) = p and p is a prime. In this paper, we show that G…
An improved high-low method for the parabola
Zane Kun Li, Po-Lam Yung
We demonstrate a modification of the high-low method of Guth-Maldague-Wang that yields a decoupling theorem which gives the sharp estimate for the discrete restriction constant for…
Two weight estimates for difference quotients
Carlos Perez, Andreas Seeger, Brian Street +1
We prove local and global two weight estimates in which we bound difference quotients of a function in terms of certain weighted norms of its gradient.
A weighted formulation of refined decoupling and inequalities of Mizohata-Takeuchi-type for the moment curve
Anthony Carbery, Zane Kun Li, Yixuan Pang +1
Let be a compact patch of a well-curved curve in with induced Lebesgue measure , and let be the Fourier e…
Strichartz inequalities: some recent developments
Jianhui Li, Zane Kun Li, Po-Lam Yung
Strichartz inequalities, originating from Fourier restriction theory, play a central role in the analysis of dispersive partial differential equations. They serve as a cornerstone…
The Neumann problem on the Clifford torus in
Jeffrey S. Case, Eric Chen, Yi Wang +2
We discuss the solution of the Neumann problem associated with the CR Yamabe operator on a subset of the CR manifold bounded by the Clifford torus . We also d…
Function spaces for decoupling
Andrew Hassell, Pierre Portal, Jan Rozendaal +1
We introduce new function spaces that yield a natural reformulation of the decoupling inequalities for the sphere and the…
A new type of superorthogonality
Philip T. Gressman, Lillian B. Pierce, Joris Roos +1
We provide a simple criterion on a family of functions that implies a square function estimate on for every even integer . This defines a new type of superorthogona…
On Polynomial Carleson operators along quadratic hypersurfaces
Theresa C. Anderson, Dominique Maldague, Lillian B. Pierce +1
We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by , for an arbitrary non-degenerate qua…
A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem
Brian Cook, Kevin Hughes, Zane Kun Li +3
We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely…
Sobolev spaces revisited
Haim Brezis, Andreas Seeger, Jean Van Schaftingen +1
We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on , using sizes of superlevel sets of suitable difference quotients. This…
Spaces of Besov-Sobolev type and a problem on nonlinear approximation
Óscar Domínguez, Andreas Seeger, Brian Street +2
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space . The resulting spaces are identifie…
Families of functionals representing Sobolev norms
Haim Brezis, Andreas Seeger, Jean Van Schaftingen +1
We obtain new characterizations of the Sobolev spaces and the bounded variation space . The characterizations are in terms of t…
Bourgain-Brezis-Mironescu Convergence via Triebel-Lizorkin Spaces
Denis Brazke, Armin Schikorra, Po-Lam Yung
We study a convergence result of Bourgain--Brezis--Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces , and $H^{1,p} = F^{1}_{p,2…
On the strict majorant property in arbitrary dimensions
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2
In this work we study -dimensional majorant properties. We prove that a set of frequencies in satisfies the strict majorant property on for all $p…
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail
Haïm Brezis, Jean Van Schaftingen, Po-Lam Yung
In the cases where there is no Sobolev-type or Gagliardo-Nirenberg-type fractional estimate involving , we establish alternative estimates where the stron…
Improved discrete restriction for the parabola
Shaoming Guo, Zane Kun Li, Po-Lam Yung
Using ideas from Guth-Maldague-Wang and working over , we show that the discrete restriction constant for the parabola is $O_{\varepsilon}((\log M)^{2 + \varepsilon})…
A new formula for the norm
Qingsong Gu, Po-Lam Yung
Recently, Brezis, Van Schaftingen and the second author established a new formula for the norm of a function in . The formula was obtain…
Limiting Sobolev and Hardy inequalities on stratified homogeneous groups
Jean Van Schaftingen, Po-Lam Yung
We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known canc…
A surprising formula for Sobolev norms
Haim Brezis, Jean Van Schaftingen, Po-Lam Yung
We establish the equivalence between the Sobolev semi-norm and a quantity obtained when replacing the strong by a weak norm in the Gagliardo semi-n…
A short proof of decoupling for the moment curve
Shaoming Guo, Zane Kun Li, Po-Lam Yung +1
We give a short and elementary proof of the decoupling inequality for the moment curve in , using a bilinear approach inspired by the nested efficient cong…
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…
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 .