Coefficient Estimates for Analytic Functions Subordinate to the Four-Leaf Domain

In recent years, various geometric domains have been employed to define subclasses of analytic functions aimed at deriving sharp estimates for the Taylor--Maclaurin coefficients. In this paper, we introduce and investigate a novel subclass of analytic functions associated with the four-leaf domain, which is symmetric about the real axis. For this class, we determine sharp coefficient estimates, establish Fekete--Szeg\"o inequalities and present generalized Zalcman-type functionals, along with estimates of Hankel determinants of prescribed order. Furthermore, we derive results for inverse functions and logarithmic coefficients. As an application, we introduce a generalized Hadamard product subclass and apply the derived results to generating functions associated with the Poisson, Pascal and Borel distributions. Connections to previously established results are also discussed.