Sharp growth conditions for boundedness of maximal function in generalized Orlicz space
: Harjulehto Petteri, Karppinen Arttu
Publisher: Suomen matemaattinen yhdistys ry
: Helsinki
: 2022
: Annales Fennici Mathematici
: 47
: 1
: 489
: 505
: 2737-114X
DOI: https://doi.org/10.54330/afm.115122
: https://doi.org/10.54330/afm.115122
: 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 .