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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Constructive decomposition of functions
of finite central mean oscillation


Author: J. D. Lakey
Journal: Proc. Amer. Math. Soc. 127 (1999), 2375-2384
MSC (1991): Primary 42B20, 42B30
Published electronically: April 8, 1999
MathSciNet review: 1486741
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Abstract: The space CMO of functions of finite central mean oscillation is an analogue of BMO where the condition that the sharp maximal function is bounded is replaced by the convergence of the sharp function at the origin. In this paper it is shown that each element of CMO is a singular integral image of an element of the Beurling space $B^{2}$ of functions whose Hardy-Littlewood maximal function converges at zero. This result is an analogue of Uchiyama's constructive decomposition of BMO in terms of singular integral images of bounded functions. The argument shows, in fact, that to each element of CMO one can construct a vector Calderón-Zygmund operator that maps that element into the proper subspace $B^{2}$.


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Additional Information

J. D. Lakey
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
Email: jlakey@nmsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04806-6
PII: S 0002-9939(99)04806-6
Keywords: Hardy space, Beurling space, singular integral, wavelets
Received by editor(s): January 31, 1997
Received by editor(s) in revised form: November 1, 1997
Published electronically: April 8, 1999
Additional Notes: The author was supported in part by NMSU grant # RC96018
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society