REMARKS ON THE FRACTIONAL OPERATORS ON ORLICZ-MORREY SPACES

We study the fractional integral and Orlicz fractional maximal operator estimates in the second kind of Orlicz-Morrey spaces. This problem originates from the Adams and Olsen inequality in Morrey spaces. We establish the boundedness corresponding to the Adams-type and the Olsen-type inequality of the fractional operator in Orlicz-Morrey spaces under conditions of Young functions. Moreover, we construct and observe the examples of the Young functions’ triplet that satisfies the condition. This paper reinforces the boundedness theory for the fractional integrals and Orlicz fractional maximal operators in Orlicz-Morrey spaces.