A probabilistic proof of the Garnett-Jones theorem on BMO

Nicholas Th. Varopoulos

Vol. 90 (1980), No. 1, 201–221

DOI: 10.2140/pjm.1980.90.201

Abstract

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