On Conjugate Functions

Analytic functions analytic in I(C arbitrary point arc length arg Fg B₂ boundary values C₁ Consider C₂ Cauchy's integral formula class H₂(C clockwise as negative conjugate functions convex contour containing corollary to lemma corresponding counterclockwise angle defined Definition denote depends due to S. E. easily verified estimate on Ap(C exists a positive exterior normal follows function which maps Gabriel's inequality harmonic functions Hence image point inverse iv(z Jordan arc Let T₂ Lindelöf's lemma Lindelöf's theorem linear operation maps I(C modulus of continuity nontangential approach obtain P₁ P₂ peio positive and clockwise positive constant positive x-direction Proof of theorem rectifiable contour Riess Riesz inequality S. E. Warschawski S₁ s₂ satisfies v(0 Schwars's inequality smooth contour containing starshaped contour starshaped with respect tangent vector theorem 1.1 theorem due unit circle utiv w₁ Warschawski 12 z-plane Zygmund 15