On interpolation of L_p[a, b] and weighted Sobolev spaces

Zeev Ditzian

Vol. 90 (1980), No. 2, 307–323

DOI: 10.2140/pjm.1980.90.307

Abstract

The goal of this paper is to characterize the interpolation spaces between L_p[a,b] or C[a,b] and the space of functions for which W(x)f^(r)(x) belongs to L_p[a,b] or C[a,b]. In order to achieve this, for a class of weights W(x) the Peetre K functional is characterized.

Mathematical Subject Classification 2000

Primary: 46E35

Secondary: 46M35

Milestones

Received: 8 June 1979

Revised: 30 November 1979

Published: 1 October 1980