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• W2964320504 abstract "The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the L2(μ)-boundedness of certain singular integral operators to the geometric properties of the support of measure μ, 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 L2(μ)-boundedness of the operator still implies that the support of μ 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.
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• W2964320504 date "2019-07-01" @default.
• W2964320504 modified "2023-10-16" @default.
• W2964320504 title "Singular integrals unsuitable for the curvature method whose L2-boundedness still implies rectifiability" @default.
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• W2964320504 doi "https://doi.org/10.1007/s11854-019-0043-5" @default.
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