Analytic capacity, bilipschitz maps and cantor sets

Mathematical Research Letters

Volumn 10, Issue 4, 2003, Pages 515-522

  Garnett, John ^a   Verdera, Joan ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141860795     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2003.v10.n4.a10     Document Type: Article

References (12)

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3. [G1] J. Gar nett, Positive length but zero analytic capacity, Proc. Amer. Math. Soc. 24 (1970), 696-599.
4. [G2] _, Analytic capacity and measure, Lecture Notes in Mathematics, Vol. 297. Springer-Verlag, Berlin-New York, 1972.
5. [J] P. W. Jones, Square functions, Cauchy integrals, analytic capacity, and harmonic measure, Harmonic analysis and partial differential equations (El Escorial, 1987), 24-68, Lecture Notes in Math., 1384, Springer, Berlin, 1989.
6. [Ma] P. Mattila, On the analytic capacity and curvature of some Cantor sets with non-σ-finite length, Publ. Math. 40 (1996), 195-204.
7. [Me] M. S. Melnikov, Analytic capacity: a discrete approach and the curvature of measure, Sb. Math. 186 (1995), 827-846.
8. [MTV] J. Mateu, X. Tolsa, J. Verdera, The planar Cantor sets of zero analytic capacity and the local T(b)-theorem, J. Amer. Math. Soc. 16 (2003), 19-28.
9. [P] H. Pajot, Notes on analytic capacity, rectifiability, Menger curvature and the Cauchy operator, to appear in Springer Lecture Notes.
10. +, Indiana Univ. Math. J. 51 (2002), 317-343.
11. [T2] _, Painleve's problem and the semiadditivity of analytic capacity, to appear in Acta Math.
12. [V] J. Verdera, On the T(1)-theorem for the Cauchy integral, Ark. Mat. 38 (2000), 183-199.