We investigate the -spectrum of linear operators defined consistently on for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the -spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω,μ); the balls with respect to this semi-metric are required to satisfy a subexponential volume growth condition. We show how previous results on -spectral independence can be treated as special cases of our results and give examples-including strictly elliptic operators in Euclidean space and generators of semigroups that satisfy (generalized) Gaussian bounds-to indicate improvements.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-11,
author = {Peer C. Kunstmann and Hendrik Vogt},
title = {Weighted norm estimates and $L\_{p}$-spectral independence of linear operators},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {129-146},
zbl = {1126.35034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-11}
}
Peer C. Kunstmann; Hendrik Vogt. Weighted norm estimates and $L_{p}$-spectral independence of linear operators. Colloquium Mathematicae, Tome 107 (2007) pp. 129-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-11/