The Cauchy transform on bounded domains
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- by J. M. Anderson and A. Hinkkanen
- Proc. Amer. Math. Soc. 107 (1989), 179-185
- DOI: https://doi.org/10.1090/S0002-9939-1989-0972226-5
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Abstract:
Suppose that $f$ is in ${L^2}(\Delta )$ where $\Delta$ is the unit disk, and that $f = 0$ outside $\Delta$. We show that then the Cauchy transform $\mathcal {C} f$ of $f$, when restricted to $\Delta$, satisfies $||\mathcal {C} f|{|_2} \leq (2/\alpha )||f|{|_2}$, where $\alpha \approx 2.4048$ is the smallest positive zero of the Bessel function ${J_0}$. This inequality is sharp.References
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Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 179-185
- MSC: Primary 30E20; Secondary 47G05
- DOI: https://doi.org/10.1090/S0002-9939-1989-0972226-5
- MathSciNet review: 972226