A1 Refereed original research article in a scientific journal
Sharp growth conditions for boundedness of maximal function in generalized Orlicz space
Authors: Harjulehto Petteri, Karppinen Arttu
Publisher: Suomen matemaattinen yhdistys ry
Publishing place: Helsinki
Publication year: 2022
Journal: Annales Fennici Mathematici
Volume: 47
Issue: 1
First page : 489
Last page: 505
eISSN: 2737-114X
DOI: https://doi.org/10.54330/afm.115122
Web address : https://doi.org/10.54330/afm.115122
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/174956943
We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function satisfies the standard continuity properties (A0), (A1) and (A2). We show that if the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space to itself then is almost increasing for large for some . Moreover we show that the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space to itself if and only if is weakly equivalent to a generalized Orlicz function satisfying (A0), (A1) and (A2) for which is almost increasing for all and some .
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