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We investigate the commutators $[b,I_{\rho}]$ of generalized fractionalintegral operators $I_{\rho}$ with functions $b$ in generalized Campanatospaces and give a necessary and sufficient condition for the boundedness of thecommutators on Orlicz spaces. To do this we define Orlicz spaces withgeneralized Young functions and prove the boundedness of generalized fractionalmaximal operators on the Orlicz spaces.

Generalized fractional integral operators and their commutators with functions in generalized Campanato spaces on Orlicz spaces