A boundedness criterion for general maximal operators
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2010
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Universitat Autònoma de Barcelona, Departament de Matemàtiques
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Lerner, A. K., y S. Ombrosi. «A Boundedness Criterion for General Maximal Operators». Publicacions Matemàtiques, vol. 54, enero de 2010, pp. 53-71. DOI.org (Crossref), https://doi.org/10.5565/PUBLMAT_54110_03.
Abstract
We consider maximal operators MB with respect to a basis B. In the case when MB satisfies a reversed weak type inequality, we obtain a boundedness criterion for MB on an arbitrary quasiBanach function space X. Being applied to specific 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 Lpw.