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Integral Equations and Operator Theory

, Volume 52, Issue 4, pp 465–475 | Cite as

Norm Estimate of the Cauchy Transform on L P (Ω)

  • Milutin R. Dostanić
Original Paper

Abstract.

We give two sided estimates of the norm of Cauchy transform on L p (Ω)(1 ≤ p < ∞) in the case when Ω is the unit disc or the bounded simply connected domain with piecewise C1 boundary. As a consequence we get the better constant in Poincare inequality. Also, we conjecture the exact value norm of Cauchy transform on L p (D), where D is the unit disc.

Mathematics Subject Classification (2000).

Primary 42B20 42B38 

Keywords.

Cauchy transform Poincare inequality Bessel functions 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Matematički Fakultet BeogradSerbia

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