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- W2336674883 abstract "This is a survey on the interplay between the structure of removable singularities of bounded analytic functions and of Lipschitz harmonic functions, behaviour of Cauchy and Riesz singular integrals on m-dimensional subsets of R n , and rectifiability properties of sets. AMS 2000 Subject Classification: Primary 28A75, 42B20. In this brief survey I discuss the interplay between the structure of removable singularities of bounded analytic functions and of Lipschitz harmonic functions, behaviour of singular integrals on m-dimensional subsets of R n , and rectifiability. I begin with 1-dimensional sets and kernels. In this case the results are pretty complete for the Cauchy kernel and the removability questions due to a special tool, Menger curvature. For much more of recent developments and further references on this topic, see the lecture notes of Pajot [20] and the survey of Tolsa [23]. Then I shall discuss the much less complete results and open problems for higher dimensional sets and Riesz kernels. I shall mostly consider m-dimensional AD- (Ahlfors‐David-) regular closed subsets of R n . This means that there is a constant C such that" @default.
- W2336674883 created "2016-06-24" @default.
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- W2336674883 date "2009-01-01" @default.
- W2336674883 modified "2023-09-24" @default.
- W2336674883 title "REMOVABILITY, SINGULAR INTEGRALS AND RECTIFIABILITY" @default.
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