A random construction of weights yields, with high probability, sharp epsilon-loss Mizohata-Takeuchi estimates for the Fourier extension operator.
On the $N$-set occupancy problem
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We explore variants of the following open question: Split $[0,1]^2$ into $N^2$ squares with side length $1/N$. Is there a way to select $N$ such squares such that each line intersects only $O(1)$ of them?
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Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type
A random construction of weights yields, with high probability, sharp epsilon-loss Mizohata-Takeuchi estimates for the Fourier extension operator.