The principal aim of this note is to prove a covering Lemma in . As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds . We will get the upper bound estimate for , where is the solution to , for and is the Laplacian on . A covering lemma in homogeneous spaces is also obtained in this note.
Cite this article
Guozhen Lu, Covering Lemmas and HMO Estimates for Eigenfunctions on Riemannian Surfaces. Rev. Mat. Iberoam. 7 (1991), no. 3, pp. 221–246DOI 10.4171/RMI/111