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

Abstract:

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 Poincaré-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.