On the maximum modulus theorem for nonanalytic functions in several complex variables.
Let w = f(z, ..., z) = u(x, ..., y) + iv(x, ..., y) be a complex function of the n complex variables z, ..., z, defined in some open set A ⊂ C. 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 x and y, nor the conditions f = 0 in A for k = 1, 2, ..., n (the Cauchy-Riemann equations in complex form).