David Beltran

activity

20182021

collaborators

8 papers

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

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

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…

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

Sobolev improving for averages over curves in R4

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

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

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

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