Fractional maximal operator in Orlicz spaces

Abstract

This work studies the fractional maximal operator acting between Orlicz spaces. The necessary and sufficient conditions for the existence of optimal target and domain spaces are established and the explicit formulas for corresponding optimal Young functions are presented.

Also, we characterize whether the operator is bounded between two given Orlicz spaces. (C) 2019 Elsevier Inc. All rights reserved.

Keywords

• Fractional maximal operator
• Orlicz spaces
• Reduction theorem
• Optimality