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Hilbert and Poincaré-Bertrand Formulas in Polyanalytic Function Theory Involving Higher Order Lipschitz Classes
Complex Analysis and Operator Theory ( IF 0.8 ) Pub Date : 2021-07-05 , DOI: 10.1007/s11785-021-01140-4 Juan Bory-Reyes 1 , Ricardo Abreu-Blaya 2 , Marco Antonio Pérez-de la Rosa 3 , Baruch Schneider 4
中文翻译:
涉及高阶 Lipschitz 类的多分析函数理论中的 Hilbert 和 Poincaré-Bertrand 公式
更新日期:2021-07-06
Complex Analysis and Operator Theory ( IF 0.8 ) Pub Date : 2021-07-05 , DOI: 10.1007/s11785-021-01140-4 Juan Bory-Reyes 1 , Ricardo Abreu-Blaya 2 , Marco Antonio Pérez-de la Rosa 3 , Baruch Schneider 4
Affiliation
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.
中文翻译:
涉及高阶 Lipschitz 类的多分析函数理论中的 Hilbert 和 Poincaré-Bertrand 公式
在目前的工作中,我们在涉及高阶 Lipschitz 类的一维复分析中获得了迭代 Cauchy-Riemann 算子单位圆上的希尔伯特公式的一些类似物。此外,还导出了与平滑有界域边界上的对应奇异迭代柯西积分相关的庞加莱-伯特兰公式,也涉及高阶 Lipschitz 类。