Geodesic
On the Boundary Properties of Solutions to the Generalized Cauchy--Riemann Equation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 142-152.

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The paper continues the study of boundary properties of polyanalytic functions and their holomorphic components started by the authors in 1998. Integral formulas for polyanalytic functions and their components as well as some generalizations of the Cauchy integral formula to polyanalytic functions are obtained. For polyanalytic and polyharmonic functions, special mean value theorems and a local maximum principle are proved. Some growth estimates for formal derivatives of polyanalytic (in particular, polyrational) functions and for their components near the boundary of their domain are found. For biharmonic functions, necessary conditions for a local extremum are pointed out. 
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E. P. Dolzhenko; V. I. Danchenko. On the Boundary Properties of Solutions to the Generalized Cauchy--Riemann Equation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 142-152. http://geodesic.mathdoc.fr/item/TM_2002_236_a14/

[1] Dolzhenko E. P., “O granichnom povedenii komponent polianaliticheskoi funktsii”, Mat. zametki, 63:6 (1998), 821–834 | MR | Zbl

[2] Dolzhenko E. P., Danchenko V. I., “O granichnom povedenii reshenii obobschennogo uravneniya Koshi–Rimana”, Vestn. MGU. Matematika. Mekhanika, 1998, no. 3, 16–25 | MR | Zbl

[3] Ramazanov A. K., “Predstavlenie prostranstva polianaliticheskikh funktsii v vide pryamoi summy ortogonalnykh podprostranstv. Prilozhenie k ratsionalnym approksimatsiyam”, Mat. zametki, 66:5 (1999), 741–759 | MR | Zbl

[4] Ramazanov A. K., “Otsenka normy polianaliticheskoi funktsii cherez normu ee poligarmonicheskoi sostavlyayuschei”, Sovremennye metody teorii funktsii i smezhnye problemy, Tez. dokl., Izd. VGU, Voronezh, 1999, 163.

[5] Balk M. B., Polyanalytic functions, Akad. Verl., Berlin, 1991 | MR | Zbl

[6] Danchenko V. I., “O ratsionalnykh sostavlyayuschikh meromorfnykh funktsii i ikh proizvodnykh”, Anal. Math., 16:4 (1990), 241–255 | DOI | MR | Zbl