Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

Autores: Guozhen Lu
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 7, Nº 3, 1991, págs. 221-246
Idioma: inglés
DOI: 10.4171/rmi/111
Títulos paralelos:
- Lemas de cubrimiento y estimaciones de la norma BMO para autofunciones en superficies riemannianas.
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Resumen
- 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 ?u + ?u = 0, for ? > 1 and ? is the Laplacian on (M2, g). A covering lemma on homogeneous spaces is also obtained in this note.