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Weak weighted inequalities for a dyadic one-sided maximal function in $ \mathbb{R} ^{n}$

Author(s): Sheldy Ombrosi
Journal: Proc. Amer. Math. Soc. 133 (2005), 1769-1775.
MSC (2000): Primary 42B25; Secondary 28B99
Posted: January 14, 2005
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Abstract: In this note we introduce a dyadic one-sided maximal function defined as

\begin{displaymath}M^{+,d}f(x)=\sup_{Q\;dyadic\text{:}x\in Q}\frac{1}{\left\vert Q\right\vert } \int_{Q^{+}}\left\vert f\right\vert ,\end{displaymath}

where $Q^{+}$ is a certain cube associated with the dyadic cube $Q$ and $f\in L_{loc}^{1}\left( \mathbb{R} ^{n}\right) $. We characterize the pair of weights $\left( w,v\right) $ for which the maximal operator $M^{+,d}$ applies $L^{p}\left( v\right) $ into weak- $ L^{p}\left( w\right) $ for $1\leq p<\infty $.

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Additional Information:

Sheldy Ombrosi
Affiliation: Departamento de Matemática, Universidad Nacional del Sur, Avenida Alem 1253, Bahía Blanca, Buenos Aires, Argentina
Email: sombrosi@uns.edu.ar

DOI: 10.1090/S0002-9939-05-07830-5
PII: S 0002-9939(05)07830-5
Keywords: Weights, dyadic one-sided maximal function
Received by editor(s): February 19, 2004
Posted: January 14, 2005
Communicated by: Andreas Seeger
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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