  In this paper, we investigate universal estimates for eigenvalues of a
buckling problem. For a bounded domain in a Euclidean space, we give a positive
contribution for obtaining a sharp universal inequality for eigenvalues of the
buckling problem. For a domain in the unit sphere, we give an important
improvement on the results of Wang and Xia [J. Funct. Anal. 245(2007),
334-352].
