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pro vyhledávání: '"Quilodran, René"'
Autor:
Quilodrán, René
We prove the existence of functions that extremize the endpoint $L^2$ to $L^4$ adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space $\mathbb{R}^4$ and that, taking symmetries into consideration, any extremizing seq
Externí odkaz:
http://arxiv.org/abs/2207.10587
We prove that constant functions are the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Fourier restriction inequalities on the unit sphere $\mathbb{S}^{d-1}\subset\mathbb{R}^d$, $d\in\{3,4,5,6,7\}$, where $n\geq 3$ is an integer. The pro
Externí odkaz:
http://arxiv.org/abs/1909.10230
Let $\mathbb{S}^{d-1}$ denote the unit sphere in Euclidean space $\mathbb{R}^d$, $d\geq 2$, equipped with surface measure $\sigma_{d-1}$. An instance of our main result concerns the regularity of solutions of the convolution equation \[ a\cdot(f\sigm
Externí odkaz:
http://arxiv.org/abs/1909.10220
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Publikováno v:
Analysis & PDE 13 (2020) 477-526
We investigate a class of sharp Fourier extension inequalities on the planar curves $s=|y|^p$, $p>1$. We identify the mechanism responsible for the possible loss of compactness of nonnegative extremizing sequences, and prove that extremizers exist if
Externí odkaz:
http://arxiv.org/abs/1804.11291
Publikováno v:
Math. Proc. Camb. Phil. Soc. 169 (2020) 307-322
We establish the general form of a geometric comparison principle for $n$-fold convolutions of certain singular measures in $\mathbb{R}^d$ which holds for arbitrary $n$ and $d$. This translates into a pointwise inequality between the convolutions of
Externí odkaz:
http://arxiv.org/abs/1804.10463
Publikováno v:
Trans. Amer. Math. Soc. (2018)
For an appropriate class of convex functions $\phi$, we study the Fourier extension operator on the surface $\{(y, |y|^2+\phi(y)):y\in\mathbb{R}^2\}$ equipped with projection measure. For the corresponding extension inequality, we compute optimal con
Externí odkaz:
http://arxiv.org/abs/1606.02623
Publikováno v:
In Journal of Functional Analysis 1 April 2021 280(7)
Autor:
Quilodrán, René
Publikováno v:
J. Analyse Math., Volume 125 (2015), no. 1, 37-70
We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that
Externí odkaz:
http://arxiv.org/abs/1108.6324
Autor:
Quilodrán, René
It is known that extremizers for the $L^2$ to $L^6$ adjoint Fourier restriction inequality on the cone in $\mathbb{R}^3$ exist. Here we show that nonnegative extremizing sequences are precompact, after the application of symmetries of the cone. If we
Externí odkaz:
http://arxiv.org/abs/1108.6081