Weighted norm estimates and $L_{p}$-spectral independence of linear operators

• Autorzy: Peer C. Kunstmann , Hendrik Vogt
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 35P05: General topics in linear spectral theory
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 1
• Strony: 129-146

Daty

wydano

2007

Twórcy

autor

Peer C. Kunstmann

• Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128 Karlsruhe, Germany

autor

Hendrik Vogt

• Institut für Analysis, Fachrichtung Mathematik, Technische Universität Dresden, D-01062 Dresden, Germany

Identyfikatory

DOI

10.4064/cm109-1-11