Corrigendum to “Improvements on Sawyer‐type estimates for generalized maximal functions”

The purpose of this note is to correct a mixed estimate involving the generalized maximal function MΦ$M_\Phi$, when Φ is a Young function satisfying certain properties. The family considered include LlogL$L\,\text{log}\,L$ type functions. Although the obtained estimates turn out to be slightly diffe...

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-12, Vol.296 (12), p.5786-5788
Main Authors: Berra, Fabio, Carena, Marilina, Pradolini, Gladis
Format: Article
Language:English
Subjects:
maximal operators
Muckenhoupt weights
Young functions
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Summary:The purpose of this note is to correct a mixed estimate involving the generalized maximal function MΦ$M_\Phi$, when Φ is a Young function satisfying certain properties. The family considered include LlogL$L\,\text{log}\,L$ type functions. Although the obtained estimates turn out to be slightly different, they are still good extensions of mixed inequalities for the classical Hardy–Littlewood maximal operators corresponding to the power functions Φ(t)=tr$\Phi (t)=t^r$, with r≥1$r\ge 1$. They also allow us to derive the boundedness properties of MΦ$M_\Phi$ between Lebesgue spaces by using interpolation techniques related to endpoint estimates of modular type.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200525