Hilbert and Poincaré-Bertrand Formulas in Polyanalytic Function Theory Involving Higher Order Lipschitz Classes
2021
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.
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