On the necessity of bump conditions for the two-weighted maximal inequality
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- by Lenka Slavíková PDF
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Abstract:
We study the necessity of bump conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$ spaces with different weights. The conditions in question are obtained by replacing the $L^{p’}$-average of $\sigma ^{\frac {1}{p’}}$ in the Muckenhoupt $A_p$-condition by an average with respect to a stronger Banach function norm, and are known to be sufficient for the two-weighted maximal inequality. We show that these conditions are in general not necessary for such an inequality to be true.References
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Additional Information
- Lenka Slavíková
- Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
- Address at time of publication: Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA
- MR Author ID: 988775
- Email: slavikoval@missouri.edu
- Received by editor(s): September 29, 2015
- Received by editor(s) in revised form: February 4, 2016
- Published electronically: September 30, 2016
- Additional Notes: This research was partly supported by the grant P201-13-14743S of the Grant Agency of the Czech Republic.
- Communicated by: Alexander Iosevich
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 109-118
- MSC (2010): Primary 42B25; Secondary 42B35
- DOI: https://doi.org/10.1090/proc/13355
- MathSciNet review: 3565364