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Maximal operators and B.M.O. for Banach lattices*

Published online by Cambridge University Press:  20 January 2009

J. García-Cuerva ,
R. A. Macías  and
J. L. Torrea
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Abstract

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We investigate the behaviour of the classical (non-smooth) Hardy-Littlewood maximal operator in the context of Banach lattices. We are mainly concerned with end-point results for p = ∞. Naturally, the main role is played by the space BMO. We analyze the range of the maximal operator in BMOx. This turns out to depend strongly on the convexity of the Banach lattice . We apply these results to study the behaviour of the commutators associated to the maximal operator. We also consider the parallel results for the maximal fractional integral operator.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 585 - 609
Copyright
Copyright © Edinburgh Mathematical Society 1998

Footnotes

*

The first and third authors were supported by DGICYT, Spain, under Grant PB94-149. The second author was supported by Ministerio de Educación, Spain, under Sabattical Grant SB—.

References

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