In the context of twistor theory, it is known that there is a one-to-one correspondence between solutions of the wave equation on the three-dimensional de Sitter space and smooth functions satisfying a certain condition on the two-sphere. This correspondence is explicitly described via specific integral transforms. In this paper, we deal with a higher dimensional case, and we establish a correspondence from smooth functions on the three-sphere to solutions of the wave equation on the four-dimensional de Sitter space. This will be of interesting issue from a point of view of mathematical physics, too.

twistor method, indefinite metric, de Sitter space, wave equation, integral transform.