Hilbert and Poincaré-Bertrand Formulas in Polyanalytic Function Theory Involving Higher Order Lipschitz Classes

In the present work we obtain some analogues of the Hilbert formulas on the unit circle for iterated Cauchy-Riemann operator in one-dimensional complex analysis involving higher order Lipschitz classes. Furthermore, a Poincare-Bertrand formula related to the corresponding singular iterated Cauchy integral over the boundary of a smoothly bounded domain is derived also involving higher order Lipschitz classes.