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- W2903730112 abstract "A theorem of Dorronsoro from 1985 quantifies the fact that a Lipschitz function $f colon mathbb{R}^{n} to mathbb{R}$ can be approximated by affine functions almost everywhere, and at sufficiently small scales. This paper contains a new, purely geometric, proof of Dorronsoro's theorem. In brief, it reduces the problem in $mathbb{R}^{n}$ to a problem in $mathbb{R}^{n - 1}$ via integralgeometric considerations. For the case $n = 1$, a short geometric proof already exists in the literature. A similar proof technique applies to parabolic Lipschitz functions $f colon mathbb{R}^{n - 1} times mathbb{R} to mathbb{R}$. A natural Dorronsoro estimate in this class is known, due to Hofmann. The method presented here allows one to reduce the parabolic problem to the Euclidean one, and to obtain an elementary proof also in this setting. As a corollary, I deduce an analogue of Rademacher's theorem for parabolic Lipschitz functions." @default.
- W2903730112 created "2018-12-22" @default.
- W2903730112 creator A5091472615 @default.
- W2903730112 date "2018-11-05" @default.
- W2903730112 modified "2023-09-27" @default.
- W2903730112 title "An integralgeometric approach to Dorronsoro estimates" @default.
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