On Weighted Solutions to (partial derivative)over-bar-Equation in the Upper Half-Plane

The paper considers the equation partial derivative f(w)/partial derivative(w) over bar = u(w) in the upper half-plane Pi(+). For a function u belonging to the class C-k(k = 1, 2, 3, ..., infinity) and the weighted space L-p(1 <= p < infinity) with a weight of type (Imw)(alpha)vertical bar w + i vertical bar(-gamma), w is an element of Pi(+), a family of solutions f(beta) depending on the complex parameter beta is constructed.