In this note, we study the connection between the fractional Laplacian operator that appeared in the recent
work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry.
González, M.; Chang, Sun-Yung Alice. Fractional Laplacian in conformal geometry. "Advances in mathematics", 30 Gener 2011, vol. 226, núm. 2, p. 1410-1432.