A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Sharp growth conditions for boundedness of maximal function in generalized Orlicz space
Tekijät: Harjulehto Petteri, Karppinen Arttu
Kustantaja: Suomen matemaattinen yhdistys ry
Kustannuspaikka: Helsinki
Julkaisuvuosi: 2022
Journal: Annales Fennici Mathematici
Vuosikerta: 47
Numero: 1
Aloitussivu: 489
Lopetussivu: 505
eISSN: 2737-114X
DOI: https://doi.org/10.54330/afm.115122
Verkko-osoite: https://doi.org/10.54330/afm.115122
Rinnakkaistallenteen osoite: 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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