Fractional Maximal Operator in Orlicz spaces
arXiv:1805.00763 · doi:10.1016/j.jmaa.2019.01.034
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.
23 pages