R. Kesler

activity

20102018

most citedSparse Bounds for the Discrete Cubic Hilbert Transform

13 citations · 61 across the 11 of their papers we have counts for

collaborators

14 papers

math.CA2018★ 6 cited

Lacunary Discrete Spherical Maximal Functions

Robert Kesler, Michael T. Lacey, Dario Mena

We prove new $ℓ^{p} (Z^{d})$ bounds for discrete spherical averages in dimensions $d \geq 5$ . We focus on the case of lacunary radii, first for general lacunary radii…

math.CA2018★ 9 cited

Sparse Bounds for the Discrete Spherical Maximal Function

Robert Kesler, Michael T. Lacey, Darío Mena

We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proo…

math.CA2018★ 3 cited

$ℓ^{p} (Z^{d})$ -Improving Properties and Sparse Bounds for Discrete Spherical Maximal Means, Revisited

Robert Kesler

We prove an expanded range of $ℓ^{p} (Z^{d})$ -improving properties and sparse bounds for discrete spherical maximal means in every dimension $d \geq 6$ . Essential elements…

math.CA2018★ 4 cited

$ℓ^{p} (Z^{d})$ -Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages

Robert Kesler

We exhibit a range of $ℓ^{p} (Z^{d})$ -improving properties for the discrete spherical maximal average in every dimension $d \geq 5$ . The strategy used to show these improv…

math.CA2018★ 5 cited

$ℓ^{p}$ -improving inequalities for Discrete Spherical Averages

Robert Kesler, Michael T. Lacey

Let $λ^{2} \in N$ , and in dimensions $d \geq 5$ , let $A_{λ} f (x)$ denote the average of $f : Z^{d} \to R$ over the lattice points on the sphere of…

math.CA2017★ 11 cited

Sparse Endpoint Estimates for Bochner-Riesz Multipliers on the Plane

Robert Kesler, Michael T. Lacey

For $0 < λ < \frac{1}{2}$ , let $B_{λ}$ be the Bochner-Riesz multiplier of index $λ$ on the plane. Associated to this multiplier is the critical index $1 < p_λ= \frac{4} {3+2 λ} < \f…

math.CA2017★ 2 cited

Sparse Bounds for Discrete Quadratic Phase Hilbert Transform

Robert Kesler, Darío Mena

Consider the discrete quadratic phase Hilbert Transform acting on $ℓ^{2}$ finitely supported functions $H^{α} f (n) := m \neq = 0 \sum \frac{e ^{2 π i α m^{2}} f ( n - m )}{m} .$ We pro…

math.CA2016★ 13 cited

Sparse Bounds for the Discrete Cubic Hilbert Transform

Amalia Culiuc, Robert Kesler, Michael T. Lacey

Consider the discrete cubic Hilbert transform defined on finitely supported functions $f$ on $Z$ by \begin{eqnarray*} H_3f(n) = \sum_{m \not = 0} \frac{f(n- m^3)}{m}. \end…

math.CA2016

Generic Multilinear Multipliers Associated to Degenerate Simplexes

Robert M. Kesler

For each $1 \leq p \leq \infty$ , let $W_{p} (R) = {f \in L^{p} (R) : f^\in L^{p^{'}} (R)}$ with norm $||f||_{W_{p}(\mathbb{R})} = ||\ha…

math.CA2016

Unboundedness Theorems for Symbols Adapted to Large Subspaces

Robert M. Kesler

For every integer $n \geq 3$ , we prove that the n-sublinear generalization of the Bi-Carleson operator of Muscalu, Tao, and Thiele given by nC^{\vecα} :(f_1,..., f_n) \mapsto \sup_…

math.CA2016

L^p Estimates for Semi-Degenerate Simplex Multipliers

Robert M. Kesler

Muscalu, Tao, and Thiele prove $L^{p}$ estimates for the "Biest" operator defined on Schwartz functions by the map \begin{align*} \hspace{5mm} C^{1,1,1}:& (f_1, f_2, f_3) \mapsto \in…

math.CA2016

Restricted Carleson Variations at Endpoint and Discretized Hilbert Transforms in the Plane

Robert M. Kesler

We provide elementary proofs that the 2-variation Carleson operator $V_{2}$ along with explicit bilinear multipliers adapted to ${ξ_{1} + ξ_{2} = 0}$ satisfy no $L^{p}$ estimates. Furthe…

math.CA2013★ 8 cited

Mixed Estimates for Degenerate Multilinear Operators Associated to Simplexes

Robert Kesler

We prove that the degenerate trilinear operator $C_{3}^{- 1, 1, 1}$ given by the formula \begin{eqnarray*} C_3^{-1,1,1}(f_1, f_2, f_3)(x)=\int_{x_1 < x_2 < x_3} \hat{f_1}(x_1) \hat{f_2}…

math.CA2010

Quantum Mechanics on Laakso Spaces

Chritopher Kauffman, Robert Kesler, Amanda Parshall +2

We first review the spectrum of the Laplacian operator on a general Laakso Space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potent…

Lacunary Discrete Spherical Maximal Functions

Sparse Bounds for the Discrete Spherical Maximal Function

ℓp(Zd)-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Means, Revisited

ℓp(Zd)-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages

ℓp-improving inequalities for Discrete Spherical Averages

Sparse Endpoint Estimates for Bochner-Riesz Multipliers on the Plane

Sparse Bounds for Discrete Quadratic Phase Hilbert Transform

Sparse Bounds for the Discrete Cubic Hilbert Transform

Generic Multilinear Multipliers Associated to Degenerate Simplexes

Unboundedness Theorems for Symbols Adapted to Large Subspaces

L^p Estimates for Semi-Degenerate Simplex Multipliers

Restricted Carleson Variations at Endpoint and Discretized Hilbert Transforms in the Plane

Mixed Estimates for Degenerate Multilinear Operators Associated to Simplexes

Quantum Mechanics on Laakso Spaces

$ℓ^{p} (Z^{d})$ -Improving Properties and Sparse Bounds for Discrete Spherical Maximal Means, Revisited

$ℓ^{p} (Z^{d})$ -Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages

$ℓ^{p}$ -improving inequalities for Discrete Spherical Averages