Revista Matemática Iberoamericana


Full-Text PDF (1253 KB) | Metadata | Table of Contents | RMI summary
Volume 7, Issue 3, 1991, pp. 221–246
DOI: 10.4171/RMI/111

Published online: 1991-12-31

Covering Lemmas and HMO Estimates for Eigenfunctions on Riemannian Surfaces

Guozhen Lu[1]

(1) Wayne State University, Detroit, USA

The principal aim of this note is to prove a covering Lemma in $\mathbb R^2$. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds $(M^2, g)$. We will get the upper bound estimate for $\| \mathrm {log} | u \||_{BMO}$, where $u$ is the solution to $\Delta u + \lambda u = 0$, for $\lambda > 1$ and $\Delta$ is the Laplacian on $(M^2, g)$. A covering lemma in homogeneous spaces is also obtained in this note.

No keywords available for this article.

Lu Guozhen: Covering Lemmas and HMO Estimates for Eigenfunctions on Riemannian Surfaces. Rev. Mat. Iberoam. 7 (1991), 221-246. doi: 10.4171/RMI/111