Vol. 90, No. 1, 1980

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A probabilistic proof of the Garnett-Jones theorem on BMO

Nicholas Th. Varopoulos

Vol. 90 (1980), No. 1, 201–221
Abstract

I give a probabilistic proof (via Brownian motion) of the real variable Garnett-Jones Theorem, which states that there exists some constant Cn, depending only on the dimension n, such that for all f BMO(Rn) in the John-Nirenberg class 1 we have distance (f,L) Cn (the distance being measured in the BMO norm).

Mathematical Subject Classification 2000
Primary: 60J65
Secondary: 42B30, 46E99, 60G46
Milestones
Received: 15 June 1979
Published: 1 September 1980
Authors
Nicholas Th. Varopoulos