Maximal function and generalized fractional integral operators on the weighted Orlicz-Lorentz-Morrey spaces

Abstract

We define the weighted Orlicz-Lorentz-Morrey and weak weighted Orlicz-Lorentz-Morrey spaces to generalize the Orlicz spaces, the weighted Lorentz spaces, the Orlicz-Lorentz spaces, and the Orlicz-Morrey spaces. Furthermore, necessary and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator, generalized fractional integral, and maximal operators on the weighted Orlicz-Lorentz-Morrey and weak Orlicz-Lorentz-Morrey spaces are given, based on the exploration of properties of Young functions, Bp{B}_{p} weights, and Bp,∞{B}_{p,\infty } weights. Specifying the weights and the Young functions, we recover the existing results and we obtain new results in the new and old settings.

Keywords

• hardy-littlewood maximal operator
• fractional integral operator
• fractional maximal operator
• orlicz-lorentz-morrey space
• weak orlicz-lorentz-morrey space
• 46e30
• 46b42