David Beltran

activity

20182023

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10 papers · 1 filter

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.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

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.CA2019

The circular maximal operator on Heisenberg radial functions