JournalsrmiVol. 7, No. 3pp. 221–246

Covering Lemmas and HMO Estimates for Eigenfunctions on Riemannian Surfaces

  • Guozhen Lu

    Wayne State University, Detroit, USA
Covering Lemmas and HMO Estimates for Eigenfunctions on Riemannian Surfaces cover
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Abstract

The principal aim of this note is to prove a covering Lemma in R2\mathbb R^2. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M2,g)(M^2, g). We will get the upper bound estimate for loguBMO\| \mathrm {log} | u \||_{BMO}, where uu is the solution to Δu+λu=0\Delta u + \lambda u = 0, for λ>1\lambda > 1 and Δ\Delta is the Laplacian on (M2,g)(M^2, g). 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. 221–246

DOI 10.4171/RMI/111