Open Access
2010 A Boundedness Criterion for General Maximal Operators
Andrei K. Lerner, Sheldy Ombrosi
Publ. Mat. 54(1): 53-71 (2010).


We consider maximal operators $M_{\mathcal B}$ with respect to a basis ${\mathcal B}$. In the case when $M_{\mathcal B}$ satisfies a reversed weak type inequality, we obtain a boundedness criterion for $M_{\mathcal B}$ on an arbitrary quasi-Banach function space $X$. Being applied to specific ${\mathcal B}$ and $X$ this criterion yields new and short proofs of a number of well-known results. Our principal application is related to an open problem on the boundedness of the two-dimensional one-sided maximal function $M^{+}$ on $L^p_w$.


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Andrei K. Lerner. Sheldy Ombrosi. "A Boundedness Criterion for General Maximal Operators." Publ. Mat. 54 (1) 53 - 71, 2010.


Published: 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1183.42024
MathSciNet: MR2603588

Primary: 42B25

Keywords: maximal operators , one-sided maximal function

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.54 • No. 1 • 2010
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