16 citations · 67 across the 27 of their papers we have counts for
30 papers
A framework for discrete bilinear spherical averages and applications to -improving estimates
Theresa C. Anderson, Angel V. Kumchev, Eyvindur A. Palsson
We decompose the discrete bilinear spherical averaging operator into simpler operators in several ways. This leads to a wide array of extensions, such as to the simplex averaging o…
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…
Weakly porous sets and Muckenhoupt distance functions
Theresa C. Anderson, Juha Lehrbäck, Carlos Mudarra +1
We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight belongs to the Mucken…
Improved bounds on number fields of small degree
Theresa C. Anderson, Ayla Gafni, Kevin Hughes +5
We study the number of degree number fields with discriminant bounded by . In this article, we improve an upper bound due to Schmidt on the number of such fields that was pr…
The structure of weight and function classes with coprime bases
Theresa C. Anderson, Chiara Travesset, Joey Veltri
In a recent work of Anderson and Hu, the authors constructed a measure that was -adic and -adic doubling, for any primes and , yet not doubling. This work relied heavi…
Discrete multilinear maximal functions and number theory
Theresa C. Anderson
Many multilinear discrete operators are primed for pointwise decomposition; such decompositions give structural information but also an essentially optimal range of bounds. We stud…
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver +3
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert…
A structure theorem on doubling measures with different bases
Theresa C. Anderson, Bingyang Hu
In this paper, we prove a structure theorem for the infinite union of -adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in…
Sharp Mei's lemma with different bases
Theresa C. Anderson, Bingyang Hu
In this paper, we prove a sharp Mei's Lemma with assuming the bases of the underlying general dyadic grids are different. As a byproduct, we specify all the possible cases of adjac…
A Structure Theorem on Intersections of General Doubling Measures and Its Applications
Theresa C. Anderson, Bingyang Hu
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit fa…
Discrete maximal operators over surfaces of higher codimension
Theresa C. Anderson, Eyvindur Ari Palsson, Angel V. Kumchev
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analy…
On the general dyadic grids in
Theresa C. Anderson, Bingyang Hu
Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson and Wei) w…
New bounds for discrete lacunary spherical averages
Theresa C. Anderson, Jose Madrid
We show that the discrete lacunary spherical maximal function is bounded on for all . Our range is new in dimension 4, where it appears that…
Sparse bounds for discrete singular Radon transforms
Theresa C. Anderson, Bingyang Hu, Joris Roos
We show that discrete singular Radon transforms along a certain class of polynomial mappings satisfy sparse bounds. For we can handle all p…
Bounds for discrete multilinear spherical maximal functions in higher dimensions
Theresa C. Anderson, Eyvindur Ari Palsson
We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions . That is, we show that this operator is bounded on $l^{p}(\mat…
Bounds for discrete multilinear spherical maximal functions
Theresa C. Anderson, Eyvindur Ari Palsson
We define a discrete version of the bilinear spherical maximal function, and show bilinear bounds for $d \ge…
Quantitative -improving for discrete spherical averages along the primes
Theresa C. Anderson
We show quantitative (in terms of the radius) -improving estimates for the discrete spherical averages along the primes. These averaging operators were defined by Anderson, Co…
On the translates of general dyadic systems on
Theresa C. Anderson, Bingyang Hu, Liwei Jiang +2
Many techniques in harmonic analysis use the fact that a continuous object can be written as a sum (or an intersection) of dyadic counterparts, as long as those counterparts belong…
Spherical means on the Heisenberg group: Stability of a maximal function estimate
Theresa C. Anderson, Laura Cladek, Malabika Pramanik +1
Consider the surface measure on a sphere in a nonvertical hyperplane on the Heisenberg group , , and the convolution . Form the associated maximal fu…
A completely integrable flow of star-shaped curves on the light cone in Lorentzian
Theresa C. Anderson, Gloria Marí Beffa
In this paper we prove that the space of differential invariants for curves with arc-length parameter in the light cone of Lorentzian , invariants under the centro-af…
A unified method for maximal truncated Calderón-Zygmund operators in general function spaces by sparse domination
Theresa C. Anderson, Bingyang Hu
In this note we give simple proofs of several results involving maximal truncated Caldeón-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function…
Improved -Boundedness for Integral -Spherical Maximal Functions
Theresa C. Anderson, Brian Cook, Kevin Hughes +1
We improve the range of -boundedness of the integral -spherical maximal functions introduced by Magyar. The previously best known bounds for the full -sp…
On the ergodic Waring--Goldbach problem
Theresa C. Anderson, Brian Cook, Kevin Hughes +1
We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring--Goldbach problem and provide several applications, including bo…
A Dyadic Gehring Inequality in Spaces of Homogeneous Type and Applications
Theresa C. Anderson, David E. Weirich
We state a version of Gehring's self improvement Theorem for reverse \Holder weights which is valid for dyadic cubes over spaces of homogeneous type and explore some of the consequ…