A simply connected domain is convex in the positive direction if for every , the half-line is contained in . We provide necessary and sufficient conditions for the existence of an angular derivative at for domains convex in the positive direction which are contained either in a horizontal half-plane or in a horizontal strip. This class of domains arises naturally in the theory of semigroups of holomorphic functions, and the existence of an angular derivative has interesting consequences for the semigroup.
"Angular derivatives and semigroups of holomorphic functions." Illinois J. Math. 63 (3) 403 - 424, October 2019. https://doi.org/10.1215/00192082-7897499