Fractional powers of operators. II. Interpolation spaces

Hikosaburo Komatsu

Vol. 21 (1967), No. 1, 89–111

DOI: 10.2140/pjm.1967.21.89

Abstract

This is a continuation of an earlier paper “Fractional Powers of Operators” published in this Journal concerning fractional powers A^α,α ∈ C, of closed linear operators A in Banach spaces X such that the resolvent (λ + A)⁻¹ exists for all λ > 0 and λ(λ + A)⁻¹ is uniformly bounded. Various integral representations of fractional powers and relationship between fractional powers and interpolation spaces, due to Lions and others, of X and domain D(A^α) are investigated.

Mathematical Subject Classification

Primary: 47.50

Secondary: 46.38

Milestones

Received: 19 November 1965

Published: 1 April 1967