Betsy Stovall

activity

20092026

most citedSome Problems in Harmonic Analysis

26 citations · 101 across the 21 of their papers we have counts for

collaborators

29 papers

math.CA2026

Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution

Chandan Biswas, Emanuel Carneiro, Taryn C. Flock +4

We identify the optimal constant and describe all maximizers for the Fourier endpoint extension inequality associated with the moment curve over finite fields. This confirms a conj…

math.CA2026

Existence of maximizers for $L^{p}$ Fourier extension from the hyperbolic paraboloid

Benjamin Bruce, Diogo Oliveira e Silva, Betsy Stovall

We prove that maximizers exist and that maximizing sequences possess subsequences that converge modulo symmetries to maximizers for the $L^{p} \to L^{q}$ Fourier extension inequalities…

math.CA2026

Bochner-Riesz means on the Heisenberg group

Detlef Müller, Lars Niedorf, Andreas Seeger +1

We prove new $L^{p}$ boundedness results for Bochner-Riesz means associated with the spectral decomposition of the sub-Laplacian on the Heisenberg group $H_{n}$ . Our results ho…

math.CA2025

Sharp endpoint extension inequalities for the moment curve on finite fields

Chandan Biswas, Emanuel Carneiro, Taryn C. Flock +3

We investigate the sharp endpoint extension inequality for the moment curve in finite fields. We determine the optimal constant and characterize the maximizers in two complementary…

math.CA2023

Sharp Fourier restriction to monomial curves

Chandan Biswas, Betsy Stovall

We establish lower bounds for the operator norms of the Fourier restriction/extension operators associated to monomial curves with affine arclength measure. Furthermore, we prove t…

math.CA2023★ 1 cited

Exponentials rarely maximize Fourier extension inequalities for cones

Giuseppe Negro, Diogo Oliveira e Silva, Betsy Stovall +1

We prove the existence of maximizers and the precompactness of $L^{p}$ -normalized maximizing sequences modulo symmetries for all valid scale-invariant Fourier extension inequalities…

math.CA2022★ 3 cited

On extremizing sequences for adjoint Fourier restriction to the sphere

Taryn C. Flock, Betsy Stovall

In this article, we develop a linear profile decomposition for the $L^{p} \to L^{q}$ adjoint Fourier restriction operator associated to the sphere, valid for exponent pairs $p < q$ for w…

math.CA2020

Existence of extremizers for Fourier restriction to the moment curve

Chandan Biswas, Betsy Stovall

We show that the restriction and extension operators associated to the moment curve possess extremizers and that $L^{p}$ -normalized extremizing sequences of these operators are preco…

math.CA2020

Variation bounds for spherical averages

David Beltran, Richard Oberlin, Luz Roncal +2

We consider $r$ -variation operators for the family of spherical means, with special emphasis on $L^{p} \to L^{q}$ estimates.

math.CA2020

Restriction inequalities for the hyperbolic hyperboloid

Benjamin Bruce, Diogo Oliveira e Silva, Betsy Stovall

In this article we establish new inequalities, both conditional and unconditional, for the restriction problem associated to the hyperbolic, or one-sheeted, hyperboloid in three di…

math.CA2019

Fourier restriction above rectangles

Jeremy Schwend, Betsy Stovall

In this article, we study the problem of obtaining Lebesgue space inequalities for the Fourier restriction operator associated to rectangular pieces of the paraboloid and perturbat…

math.CA2018★ 5 cited

Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case

Emanuel Carneiro, Diogo Oliveira e Silva, Mateus Sousa +1

We prove that in dimensions $d \geq 3$ , the non-endpoint, Lorentz-invariant $L^{2} \to L^{p}$ adjoint Fourier restriction inequality on the $d$ -dimensional hyperboloid $\mathbb{H}^d \s…

math.CA2018★ 12 cited

Extremizability of Fourier restriction to the paraboloid

Betsy Stovall

In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $R^{1 + d}$ have extremizers and that $L^{p}$ -normalized extremizi…

math.CA2017

Quasi-extremals for convolution with surface measure on the sphere

Betsy Stovall

If $T$ is the operator given by convolution with surface measure on the sphere, $(E, F)$ is a quasi-extremal pair of sets for $T$ if $\langle Tχ_E, χ_F \rangle \gtrsim |E|^{d/(d+1)}…

math.CA2017★ 13 cited

Scale invariant Fourier restriction to a hyperbolic surface

Betsy Stovall

This result sharpens the bilinear to linear deduction of Lee and Vargas for extension estimates on the hyperbolic paraboloid in $R^{3}$ to the sharp line, leading to the firs…

math.CA2017

Linear and bilinear restriction to certain rotationally symmetric hypersurfaces

Betsy Stovall

Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining po…

math.CA2017★ 5 cited

Uniform estimates for Fourier restriction to polynomial curves in $R^{d}$

Betsy Stovall

We prove uniform $L^{p} \to L^{q}$ bounds for Fourier restriction to polynomial curves in $R^{d}$ with affine arclength measure, in the conjectured range.

math.CA2017

Uniform $L^{p}$ -improving for weighted averages on curves

Betsy Stovall

We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal $L^{p}$ -improving estimates for associated multilinear generalized Radon trans…

math.CA2017

Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

Spyridon Dendrinos, Betsy Stovall

We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euc…

math.CA2017

$L^{p}$ improving multilinear Radon-like transforms

Betsy Stovall

We characterize (up to endpoints) the $k$ -tuples $(p_{1}, \dots, p_{k})$ for which certain $k$ -linear generalized Radon transforms map $L^{p_{1}} \times \dots \times L^{p_{k}}$ boundedly i…

math.CA2017★ 1 cited

Endpoint $L^{p} \to L^{q}$ bounds for integration along certain polynomial curves

Betsy Stovall

We establish strong-type endpoint $L^{p} (R^{d}) \to L^{q} (R^{d})$ bounds for the operator given by convolution with affine arclength measure on polynomial curves for $d \ge…

math.CA2017

Endpoint Lebesgue estimates for weighted averages on polynomial curves

Michael Christ, Spyridon Dendrinos, Betsy Stovall +1

We establish optimal Lebesgue estimates for a class of generalized Radon transforms defined by averaging functions along polynomial-like curves. The presence of an essentially opti…

math.DG2017

Coordinates Adapted to Vector Fields: Canonical Coordinates

Betsy Stovall, Brian Street

Given a finite collection of $C^{1}$ vector fields on a $C^{2}$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate sys…

math.CA2017★ 26 cited

Some Problems in Harmonic Analysis

Loukas Grafakos, Diogo Oliveira e Silva, Malabika Pramanik +2

In May 2016, we organized a conference in harmonic analysis in honor of Professor Michael Christ, on the campus of the University of Wisconsin in Madison. We are happy to present s…

Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution

Existence of maximizers for Lp Fourier extension from the hyperbolic paraboloid

Bochner-Riesz means on the Heisenberg group

Sharp endpoint extension inequalities for the moment curve on finite fields

Sharp Fourier restriction to monomial curves

Exponentials rarely maximize Fourier extension inequalities for cones

On extremizing sequences for adjoint Fourier restriction to the sphere

Existence of extremizers for Fourier restriction to the moment curve

Variation bounds for spherical averages

Restriction inequalities for the hyperbolic hyperboloid

Fourier restriction above rectangles

Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case

Extremizability of Fourier restriction to the paraboloid

Quasi-extremals for convolution with surface measure on the sphere

Scale invariant Fourier restriction to a hyperbolic surface

Linear and bilinear restriction to certain rotationally symmetric hypersurfaces

Uniform estimates for Fourier restriction to polynomial curves in Rd

Uniform Lp-improving for weighted averages on curves

Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

Lp improving multilinear Radon-like transforms

Endpoint Lp→Lq bounds for integration along certain polynomial curves

Endpoint Lebesgue estimates for weighted averages on polynomial curves

Coordinates Adapted to Vector Fields: Canonical Coordinates

Some Problems in Harmonic Analysis

Existence of maximizers for $L^{p}$ Fourier extension from the hyperbolic paraboloid

Uniform estimates for Fourier restriction to polynomial curves in $R^{d}$

Uniform $L^{p}$ -improving for weighted averages on curves

$L^{p}$ improving multilinear Radon-like transforms

Endpoint $L^{p} \to L^{q}$ bounds for integration along certain polynomial curves