Another characterization of BLO
Author:
Colin Bennett
Journal:
Proc. Amer. Math. Soc. 85 (1982), 552-556
MSC:
Primary 42B25
DOI:
https://doi.org/10.1090/S0002-9939-1982-0660603-5
MathSciNet review:
660603
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that a locally integrable function on
has bounded lower oscillation
if and only if
, where
has bounded mean oscillation
and
a.e., and
is bounded. Here,
is a variant of the familiar Hardy-Littlewood maximal function:
(no absolute values), where
is the mean value of
over the cube
.
- [1]
C. Bennett, R. A. DeVore and R. Sharpley, Weak-
and BMO, Ann. of Math. (2) 113 (1981), 601-611. MR 621018 (82h:46047)
- [2] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254. MR 565349 (81b:42067)
- [3] C. Sadosky, Interpolation of operators and singular integrals, Dekker, New York, 1979. MR 551747 (81d:42001)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0660603-5
Article copyright:
© Copyright 1982
American Mathematical Society