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

DOI:
https://doi.org/10.1090/S0002-9939-99-04806-6

Published electronically:
April 8, 1999

MathSciNet review:
1486741

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Abstract | References | Similar Articles | Additional Information

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 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 .

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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:
https://doi.org/10.1090/S0002-9939-99-04806-6

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