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Journal of the London Mathematical Society 1994 49(3):529-542; doi:10.1112/jlms/49.3.529
© 1994 by London Mathematical Society
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© The London Mathematical Society

One-Sided BMO Spaces

F. J. Martín-Reyes and A. De La Torre

Análisis Matemático, Facultad de Ciencias, Universidad de Málaga 29071 Málaga, Spain

Received 29 November 1991.

In this paper we introduce the one-sided sharp functions denned by

Formula
and

Formula
where z+ = max(z, 0). We study the BMO spaces associated to Formula and Formula and their relation with the good weights for the one-sided Hardy-Littlewood maximal functions. Finally, as an application of our results, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.

E-mail: MARTIN_REYES{at}CCUMA.UMA.ES.

E-mail: TORRE_R{at}CCUMA.UMA.ES.

This research has been partially supported by D.G.I.C.Y.T. grant (PB88-0324) and Junta de Andaluíia.


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