Vol. 198, No. 2, 2001

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Boundedness of the Riesz projection on spaces with weights

Stephen D. Abbott and Irina Marinov

Vol. 198 (2001), No. 2, 257–264
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
Authors
Stephen D. Abbott
Middlebury College
Middlebury, VT 05753
Irina Marinov
Dept. of Atmospheric and Oceanic Sciences
Princeton University
Princeton, NJ 08544