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BMO, VMO, and All That Jazz: A Decomposition of Functions with Vanishing Mean Oscillation
by
Michael Korey
University of Potsdam, Germany
A function has vanishing mean oscillation (VMO) on Rn if its mean oscillation-the local average of its pointwise deviation from its mean value-both is uniformly bounded over all cubes within Rn and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. In the present talk it will be shown that each VMO function is the difference of two functions in VLO, a result which refines the corresponding decomposition of BMO functions proven by Coifman and Rochberg in 1980.
Date received: August 14, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caia-12.