52 citations · 278 across the 40 of their papers we have counts for
26 papers · 1 filter
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…
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…
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…
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…
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 .
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…
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…
Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem
Shaoming Guo, Joris Roos, Po-Lam Yung
We prove variation-norm estimates for certain oscillatory integrals related to Carleson's theorem. Bounds for the corresponding maximal operators were first proven by Stein and Wai…
Approximation in higher-order Sobolev spaces and Hodge systems
Pierre Bousquet, Emmanuel Russ, Yi Wang +1
Let be an integer, and be a differential -form on with coefficients. It was proved by Bourgain and Brezis (\cite[…
Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem
Sagun Chanillo, Jean Van Schaftingen, Po-Lam Yung
We offer a variant of a proof of a borderline Bourgain-Brezis Sobolev embedding theorem on . We use this idea to extend the result to real hyperbolic spaces $\mathbb{…
Polynomial Carleson operators along monomial curves in the plane
Shaoming Guo, Lillian B. Pierce, Joris Roos +1
We prove bounds for partial polynomial Carleson operators along monomial curves in the plane with a phase polynomial consisting of a single monomial.…
On a trilinear singular integral form with determinantal kernel
Philip Gressman, Danqing He, Vjekoslav Kovač +3
We study a trilinear singular integral form acting on two-dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the…
A polynomial Carleson operator along the paraboloid
L. B. Pierce, Po-Lam Yung
In this work we extend consideration of the polynomial Carleson operator to the setting of a Radon transform acting along the paraboloid in for . Inspi…
A sharp subelliptic Sobolev embedding theorem with weights
Po-Lam Yung
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to pro…