Boundedness of the Riesz projection on spaces with weights

Stephen D. Abbott and Irina Marinov

Vol. 198 (2001), No. 2, 257–264

DOI: 10.2140/pjm.2001.198.257

Abstract

Given a bounded, non-negative operator W and a projection P on a Hilbert space, we find necessary and sufficient conditions for the existence of a non-trivial, non-negative operator V such that P is bounded from L²(W) to L²(V ). This leads to a vector-valued version of a theorem of Koosis and Treil’ concerning the boundedness of the Riesz projection in spaces with weights.

Milestones

Received: 1 August 1999

Published: 1 April 2001