# Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

Revista Matemática Iberoamericana (1991)

- Volume: 7, Issue: 3, page 221-246
- ISSN: 0213-2230

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topLu, Guozhen. "Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.." Revista Matemática Iberoamericana 7.3 (1991): 221-246. <http://eudml.org/doc/39417>.

@article{Lu1991,

abstract = {The principal aim of this note is to prove a covering Lemma in R2. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M2, g). We will get the upper bound estimate for || log |u| ||BMO, where u is the solution to Δu + λu = 0, for λ > 1 and Δ is the Laplacian on (M2, g). A covering lemma on homogeneous spaces is also obtained in this note.},

author = {Lu, Guozhen},

journal = {Revista Matemática Iberoamericana},

keywords = {Autofunciones; Lemas de cubrimiento; Espacio homogéneo; Superficies Riemann; Variedad riemanniana; Transformada de Laplace; Medidas de Borel; BMO estimate; Laplace operator; nodal set; Riemannian manifold; covering lemma},

language = {eng},

number = {3},

pages = {221-246},

title = {Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.},

url = {http://eudml.org/doc/39417},

volume = {7},

year = {1991},

}

TY - JOUR

AU - Lu, Guozhen

TI - Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

JO - Revista Matemática Iberoamericana

PY - 1991

VL - 7

IS - 3

SP - 221

EP - 246

AB - The principal aim of this note is to prove a covering Lemma in R2. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M2, g). We will get the upper bound estimate for || log |u| ||BMO, where u is the solution to Δu + λu = 0, for λ > 1 and Δ is the Laplacian on (M2, g). A covering lemma on homogeneous spaces is also obtained in this note.

LA - eng

KW - Autofunciones; Lemas de cubrimiento; Espacio homogéneo; Superficies Riemann; Variedad riemanniana; Transformada de Laplace; Medidas de Borel; BMO estimate; Laplace operator; nodal set; Riemannian manifold; covering lemma

UR - http://eudml.org/doc/39417

ER -

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