In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces for fractional maximal functions and Riesz potentials. We prove their boundedness between generalized Orlicz spaces and give a characterization for functions of bounded mean oscillation. To best of our knowledge, these results are also new in the special case of double phase spaces.
Sobolev type inequalities for fractional maximal functions and Riesz potentials in half spaces
Boundedness of fractional maximal operator and its commutators on generalized Orlicz-Morrey spaces
A characterization for Adams type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces
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