Conformal images of Carleson curves
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- by Christopher J. Bishop HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 9 (2022), 90-94
Abstract:
We show that if $\gamma$ is a curve in the unit disk, then arclength on $\gamma$ is a Carleson measure iff the image of $\gamma$ has finite length under every conformal map of the disk onto a bounded domain with a rectifiable boundary.References
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- John B. Garnett and Donald E. Marshall, Harmonic measure, New Mathematical Monographs, vol. 2, Cambridge University Press, Cambridge, 2008. Reprint of the 2005 original. MR 2450237
Additional Information
- Christopher J. Bishop
- Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
- MR Author ID: 37290
- Email: bishop@math.sunysb.edu
- Received by editor(s): July 20, 2020
- Received by editor(s) in revised form: September 27, 2020, and November 17, 2020
- Published electronically: March 29, 2022
- Additional Notes: The author was partially supported by NSF Grant DMS 1906259.
- Communicated by: Filippo Bracci
- © Copyright 2022 by the author under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 9 (2022), 90-94
- MSC (2020): Primary 30H10
- DOI: https://doi.org/10.1090/bproc/69
- MathSciNet review: 4402047