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