A Bimonogenic Cauchy Transform on Higher Order Lipschitz Classes

Abstract:

We prove that a Cauchy transform naturally arising for bimonogenic Clifford algebra valued functions theory behaves invariant on the higher order Lipschitz classes and obtain a Plemelj–Privalov theorem for the related singular integral transform. Moreover, we obtain an upper bound for the norm of such an operator in the pathological case of fractal boundaries.

Año de publicación:

2019

Keywords:

• higher order Lipschitz classes
• Cauchy transform
• Bimonogenic functions

Fuente:

scopus