# Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind

## TL;DR

This paper characterizes the boundedness of generalized fractional integral and maximal operators on Orlicz and generalized Orlicz--Morrey spaces, including weak and specific boundedness types, advancing understanding of these operators in functional analysis.

## Contribution

It provides new characterizations of boundedness for these operators on advanced function spaces, including criteria for weak boundedness and specific boundedness types.

## Key findings

- Boundedness criteria for $I_{\rho}$ and $M_{\rho}$ on Orlicz spaces.
- Characterizations of Spanne-type and Adams-type boundedness on generalized Orlicz--Morrey spaces.
- Criteria for weak boundedness of the operators.

## Abstract

In the present paper, we will characterize the boundedness of the generalized fractional integral operators $I_{\rho}$ and the generalized fractional maximal operators $M_{\rho}$ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces.