Browsing Analysis of Partial Differential Equations (APDE) by Author "Beltran D."
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Bilinear identities involving the $k$-plane transform and Fourier extension operators
Beltran, D.; Vega, L.
(2019)
We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$-plane transform. As the estimates are $L^2$-based, they follow from ... -
Bilinear identities involving the k-plane transform and Fourier extension operators
Beltran, D.; Vega, L. (2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ... -
Endpoint Sobolev continuity of the fractional maximal function in higher dimensions
(2019)We establish continuity mapping properties of the non-centered fractional maximal operator $M_{\beta}$ in the endpoint input space $W^{1,1}(\mathbb{R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. ... -
Regularity of fractional maximal functions through Fourier multipliers
(2018)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 the spherical fractional maximal function ... -
Sparse bounds for pseudodifferential operators
(2018)We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ... -
Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
(2018)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 estimates for wave equations on compact Riemannian ... -
Variation bounds for spherical averages
Beltran, D.; Oberlin, R.; Roncal, L.; Stovall, B.; Seeger, A. (2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates