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- W2496232743 abstract "The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the $L^2(mu)$-boundedness of certain singular integral operators to the geometric properties of the support of measure $mu$, e.g. rectifiability. It can be applied however only if Menger curvature-like permutations, directly associated with the kernel of the operator, are non-negative. We give an example of an operator in the plane whose corresponding permutations change sign but the $L^2(mu)$-boundedness of the operator still implies that the support of $mu$ is rectifiable. To the best of our knowledge, it is the first example of this type. We also obtain several related results with Ahlfors-David regularity conditions." @default.
- W2496232743 created "2016-08-23" @default.
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- W2496232743 date "2016-07-26" @default.
- W2496232743 modified "2023-10-15" @default.
- W2496232743 title "Singular integrals unsuitable for the curvature method whose $L^2$-boundedness still implies rectifiability" @default.
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