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- W4292947236 abstract "Suppose $S$ is a smooth compact hypersurface in $Bbb R^n$ and $sigma$ is an appropriate measure on $S$. If $Ef= hat{fdsigma}$ is the extension operator associated with $(S,sigma)$, then the Mizohata-Takeuchi conjecture asserts that $int |Ef(x)|^2 w(x) dx leq C (sup_T w(T)) | f |_{L^2(sigma)}^2$ for all functions $f in L^2(sigma)$ and weights $w : Bbb R^n to [0,infty)$, where the $sup$ is taken over all tubes $T$ in $Bbb R^n$ of cross-section 1, and $w(T)= int_T w(x) dx$. This paper investigates how far we can go in proving the Mizohata-Takeuchi conjecture in $Bbb R^2$ if we only take the decay properties of $hat{sigma}$ into consideration. As a consequence of our results, we obtain new estimates for a class of convex curves that include exponentially flat ones such as $(t,e^{-1/t^m})$, $0 leq t leq c_m$, $m in Bbb N$." @default.
- W4292947236 created "2022-08-24" @default.
- W4292947236 creator A5015161596 @default.
- W4292947236 date "2022-08-22" @default.
- W4292947236 modified "2023-09-27" @default.
- W4292947236 title "Mizohata-Takeuchi estimates in the plane" @default.
- W4292947236 doi "https://doi.org/10.48550/arxiv.2208.10305" @default.
- W4292947236 hasPublicationYear "2022" @default.
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