David Beltran

activity

20142023

most citedVariable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds

42 citations · 104 across the 15 of their papers we have counts for

collaborators

21 papers

math.CA2023

Bochner-Riesz means at the critical index: Weighted and sparse bounds

David Beltran, Joris Roos, Andreas Seeger

We consider Bochner-Riesz means on weighted $L^{p}$ spaces, at the critical index $λ (p) = d (\frac{1}{p} - \frac{1}{2}) - \frac{1}{2}$ . For every $A_{1}$ -weight we obtain an extension of Vargas' weak…

math.CA2023

Off-diagonal estimates for the helical maximal function

David Beltran, Jennifer Duncan, Jonathan Hickman

The optimal $L^{p} \to L^{q}$ mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analys…

math.CA2023★ 1 cited

On sharp isoperimetric inequalities on the hypercube

David Beltran, Paata Ivanisvili, José Madrid

We prove the sharp isoperimetric inequality $E h_{A}^{l o g_{2} (3/2)} \geq μ (A)^{*} (lo g_{2} (1/ μ (A)^{*}))^{l o g_{2} (3/2)}$ for all sets $A \subseteq {0, 1}^{n}$ , wher…

math.CA2022★ 1 cited

Endpoint sparse domination for classes of multiplier transformations

David Beltran, Joris Roos, Andreas Seeger

We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipli…

math.AP2022★ 5 cited

$L^{p} - L^{q}$ local smoothing estimates for the wave equation via $k$ -broad Fourier restriction

David Beltran, Olli Saari

We explore the connection between $k$ -broad Fourier restriction estimates and sharp regularity $L^{p} - L^{q}$ local smoothing estimates for the solutions of the wave equation in $\mathb…

math.CA2021

Continuity of the gradient of the fractional maximal operator on $W^{1, 1} (R^{d})$

David Beltran, Cristian González-Riquelme, José Madrid +1

We establish that the map $f \mapsto ∣\nabla M_{α} f ∣$ is continuous from $W^{1, 1} (R^{d})$ to $L^{q} (R^{d})$ , where $α \in (0, d)$ , $q = \frac{d}{d - α}$ and $\mathca…

math.CA2021★ 9 cited

Sharp $L^{p}$ bounds for the helical maximal function

David Beltran, Shaoming Guo, Jonathan Hickman +1

We establish the $L^{p} (R^{3})$ boundedness of the helical maximal function for the sharp range $p > 3$ . Our results improve the previous known bounds for $p > 4$ . The key ingredi…

math.CA2021

Sobolev improving for averages over curves in $R^{4}$

David Beltran, Shaoming Guo, Jonathan Hickman +1

We study $L^{p}$ -Sobolev improving for averaging operators $A_{γ}$ given by convolution with a compactly supported smooth density $μ_{γ}$ on a non-degenerate curve. In particular, in 4 d…

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★ 12 cited

Multi-scale sparse domination

David Beltran, Joris Roos, Andreas Seeger

We prove a bilinear form sparse domination theorem that applies to many multi-scale operators beyond Calderón-Zygmund theory, and also establish necessary conditions. Among the app…

math.CA2019

The circular maximal operator on Heisenberg radial functions

David Beltran, Shaoming Guo, Jonathan Hickman +1

Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group $H^{1}$ restricted to a class of Heisenberg radial functions. Under this assu…

math.CA2019

Regularity of the centered fractional maximal function on radial functions

David Beltran, José Madrid

We study the regularity properties of the centered fractional maximal function $M_{β}$ . More precisely, we prove that the map $f \mapsto ∣\nabla M_{β} f ∣$ is bounded and continuous from…

math.CA2019★ 3 cited

Bilinear identities involving the $k$ -plane transform and Fourier extension operators

David Beltran, Luis Vega

We prove certain $L^{2} (R^{n})$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$ -plane transform. As the e…

math.CA2019

Endpoint Sobolev continuity of the fractional maximal function in higher dimensions

David Beltran, José Madrid

We establish continuity mapping properties of the non-centered fractional maximal operator $M_{β}$ in the endpoint input space $W^{1, 1} (R^{d})$ for $d \geq 2$ in the cases for…

math.AP2018

Sharp local smoothing estimates for Fourier integral operators

David Beltran, Jonathan Hickman, Christopher D. Sogge

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe so…

math.CA2018★ 22 cited

Regularity of fractional maximal functions through Fourier multipliers

David Beltran, João Pedro Ramos, Olli Saari

We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$ . We also show that…

math.AP2018★ 42 cited

Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds

David Beltran, Jonathan Hickman, Christopher D. Sogge

The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estim…

math.CA2017

Sparse bounds for pseudodifferential operators

David Beltran, Laura Cladek

We prove sparse bounds for pseudodifferential operators associated to Hörmander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis.…

math.CA2016

Control of pseudodifferential operators by maximal functions via weighted inequalities

David Beltran

We establish general weighted $L^{2}$ inequalities for pseudodifferential operators associated to the Hörmander symbol classes $S_{ρ, δ}^{m}$ . Such inequalities allow to control these o…

math.CA2015★ 9 cited

Subdyadic square functions and applications to weighted harmonic analysis

David Beltran, Jonathan Bennett

Through the study of novel variants of the classical Littlewood-Paley-Stein $g$ -functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on…

math.CA2014

A Fefferman-Stein inequality for the Carleson operator

David Beltran

We provide a Fefferman-Stein type weighted inequality for maximally modulated Calderón-Zygmund operators that satisfy \textit{a priori} weak type unweighted estimates. This inequal…

Bochner-Riesz means at the critical index: Weighted and sparse bounds

Off-diagonal estimates for the helical maximal function

On sharp isoperimetric inequalities on the hypercube

Endpoint sparse domination for classes of multiplier transformations

Lp−Lq local smoothing estimates for the wave equation via k-broad Fourier restriction

Continuity of the gradient of the fractional maximal operator on W1,1(Rd)

Sharp Lp bounds for the helical maximal function

Sobolev improving for averages over curves in R4

Variation bounds for spherical averages

Multi-scale sparse domination

The circular maximal operator on Heisenberg radial functions

Regularity of the centered fractional maximal function on radial functions

Bilinear identities involving the k-plane transform and Fourier extension operators

Endpoint Sobolev continuity of the fractional maximal function in higher dimensions

Sharp local smoothing estimates for Fourier integral operators

Regularity of fractional maximal functions through Fourier multipliers

Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds

Sparse bounds for pseudodifferential operators

Control of pseudodifferential operators by maximal functions via weighted inequalities

Subdyadic square functions and applications to weighted harmonic analysis

A Fefferman-Stein inequality for the Carleson operator

$L^{p} - L^{q}$ local smoothing estimates for the wave equation via $k$ -broad Fourier restriction

Continuity of the gradient of the fractional maximal operator on $W^{1, 1} (R^{d})$

Sharp $L^{p}$ bounds for the helical maximal function

Sobolev improving for averages over curves in $R^{4}$

Bilinear identities involving the $k$ -plane transform and Fourier extension operators