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 quasi-Banach 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.
| Original language | American English |
|---|---|
| Pages (from-to) | 53-71 |
| Journal | Publicacions Matemàtiques |
| Volume | 54 |
| Issue number | 1 |
| State | Published - 2010 |