Weighted norm estimates and $L_p$-spectral independence of linear operators

Peer C. Kunstmann, and Hendrik Vogt. "Weighted norm estimates and $L_{p}$-spectral independence of linear operators." Colloquium Mathematicae 109.1 (2007): 129-146. <http://eudml.org/doc/284312>.

@article{PeerC2007,
abstract = {We investigate the $L_\{p\}$-spectrum of linear operators defined consistently on $L_\{p\}(Ω)$ for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the $L_\{p\}$-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 $L_\{p\}$-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.},
author = {Peer C. Kunstmann, Hendrik Vogt},
journal = {Colloquium Mathematicae},
keywords = {-spectrum; weighted norm estimates; integral operators; resolvent; elliptic operators; heat kernel estimates},
language = {eng},
number = {1},
pages = {129-146},
title = {Weighted norm estimates and $L_\{p\}$-spectral independence of linear operators},
url = {http://eudml.org/doc/284312},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Peer C. Kunstmann
AU - Hendrik Vogt
TI - Weighted norm estimates and $L_{p}$-spectral independence of linear operators
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 1
SP - 129
EP - 146
AB - We investigate the $L_{p}$-spectrum of linear operators defined consistently on $L_{p}(Ω)$ for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the $L_{p}$-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 $L_{p}$-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.
LA - eng
KW - -spectrum; weighted norm estimates; integral operators; resolvent; elliptic operators; heat kernel estimates
UR - http://eudml.org/doc/284312
ER -