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3 results

10 - Singular Integrals
Pertti Mattila, University of Helsinki
Book:

Rectifiability

Published online:

19 December 2022

Print publication:

12 January 2023, pp 89-98
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Summary

Characterizations of rectifiability in terms of boundedness and principal values of the Riesz transfrom and of removable singularities of Lipschitz harmonic functions

9 - Bounded Analytic Functions and the Cauchy Transform
Pertti Mattila, University of Helsinki
Book:

Rectifiability

Published online:

19 December 2022

Print publication:

12 January 2023, pp 78-88
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Summary

Charcaterizations of rectifiability in terms of removable singularities of bounded analytic functions and of boundedness and principal values of the Cauchy transform

Each Copy of the Real Line in is Removable
E. Santillan Zeron
Journal:

Canadian Mathematical Bulletin / Volume 44 / Issue 1 / 01 March 2001

Published online by Cambridge University Press:

20 November 2018, pp. 126-128

Print publication:

01 March 2001
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Around 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of ${{\mathbb{C}}^{N}}\left( N\ge 2 \right)$ is removable for holomorphic functions, if its topological dimension is less than or equal to $N\,-\,2$. Besides, they asked whether closed subsets of ${{\mathbb{C}}^{2}}$ homeomorphic to the real line (the simplest 1-dimensional sets) are removable for holomorphic functions. In this paper we propose a positive answer to that question.