Orthonormal systems of inputs satisfy a global Mizohata-Takeuchi-type weighted inequality for the sphere and paraboloid, with an X-ray transform norm over the midpoint set K^diamond on the right-hand side.
$L^p$ weighted Fourier restriction estimates
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We obtain some sharp $L^p$ weighted Fourier restriction estimates of the form $\|Ef\|_{L^p(B^{n+1}(0,R),Hdx)} \lessapprox R^{\beta}\|f\|_2$, where $E$ is the Fourier extension operator over the truncated paraboloid, and $H$ is a weight function on $\mathbb R^{n+1}$ which is $n$-dimensional up to scale $\sqrt R$.
citation-role summary
background 1
citation-polarity summary
fields
math.CA 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Mizohata-Takeuchi inequalities for orthonormal systems
Orthonormal systems of inputs satisfy a global Mizohata-Takeuchi-type weighted inequality for the sphere and paraboloid, with an X-ray transform norm over the midpoint set K^diamond on the right-hand side.