A version of Schwarz lemma for perturbed Dirac operator in octonionic analysis

Abstract As octonionic analysis is a non-associative extension of quaternionic analysis and the perturbed Dirac operator serves as a decomposition of the Helmholtz operator, the perturbed Dirac operator in octonionic analysis has garnered significant attention. This article focuses on the integral formula and the estimation of perturbed Dirac calculations within the framework of octonionic analysis. Firstly, we present the Cauchy-Pompeiu formula for perturbed Dirac operators using Stokes’ theorem. Subsequently, by applying the aforementioned integral formula in conjunction with the Poisson integral formula, we derive the estimated value of the function that is nullified by the perturbed Dirac operator, which yields a form of the Schwarz lemma.