On the Boundary Properties of Solutions to the Generalized Cauchy–Riemann Equation

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.