TL;DR
This paper investigates the boundedness of the fractional maximal operator between Orlicz spaces, providing characterizations, conditions for optimal spaces, and explicit formulas for Young functions.
Contribution
It offers a comprehensive characterization of the fractional maximal operator's boundedness in Orlicz spaces and derives explicit formulas for optimal spaces and Young functions.
Findings
Characterization of boundedness conditions
Necessary and sufficient conditions for optimal spaces
Explicit formulas for Young functions
Abstract
We study the fractional maximal operator acting between Orlicz spaces. We characterise whether the operator is bounded between two given Orlicz spaces. Also a necessary and sufficient conditions for the existence of an optimal target and domain spaces are established and the explicit formulas of corresponding optimal Young functions are presented.
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