Lp, uniform, and Lipschitz estimates are obtained for holomorphic Sobolev functions along parts of the boundary of a smooth domain, taking into account in a precise way the shape of the boundary.

Schwarz Lemma: A classical result constraining holomorphic functions mapping the unit disc into itself, providing bounds on their absolute values and derivatives.

Holomorphic functions in Rn are defined to generalize those in R2. A Taylor formula and a Cauchy integral formula are presented. An application of the Taylor formula to the kernel of the Cauchy ...