Weighted Composition Operators from Hardy Spaces to Weighted-Type Spaces on the Upper Half-Plane

Let the holomorphic mapping ?, and the holomorphic self-map ? are on the upper half-plane. We characterize bounded weighted composition operators between the Hardy space and the weighted-type space on the upper half-plane, and we study the special cases when which is the Hilbert space. Under a mild condition on ?; we also show the compactness of these operators and there special cases. Keywords: Weighted composition operators, Hardy spaces, weighted type spaces, upper half plane