Applications To Analysis
Somewhat surprisingly, these conjectures have been shown to be connected to a number of questions in other fields, notably in harmonic analysis. For instance, in 1971, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions greater than 1, truncated Fourier integrals taken over balls centered at the origin with radii tending to infinity need not converge in Lp norm when p ≠ 2 (this is in contrast to the one-dimensional case where such truncated integrals do converge).
Read more about this topic: Kakeya Set
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