Let w = f(z1, ..., zn) = u(x1, ..., yn) + iv(x1, ..., yn) be a complex function of the n complex variables z1, ..., zn, defined in some open set A ⊂ Cn. The purpose of this note is to prove a maximum modulus theorem for a class of these functions, assuming neither the continuity of the first partial derivatives of u and v with respect to xk and yk, nor the conditions fzk = 0 in A for k = 1, 2, ..., n (the Cauchy-Riemann equations in complex form).
@article{urn:eudml:doc:39798,
title = {On the maximum modulus theorem for nonanalytic functions in several complex variables.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {41},
year = {1981},
pages = {27-30},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39798}
}
González Rodríguez, Mario O. On the maximum modulus theorem for nonanalytic functions in several complex variables.. Revista Matemática Hispanoamericana, Tome 41 (1981) pp. 27-30. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39798/