Abstract:
The paper considers the space of generalized fractional-maximal function, constructed on the basis of
a rearrangement-invariant space. Two types of cones generated by a nonincreasing rearrangement of a
generalized fractional-maximal function and equipped with positive homogeneous functionals are constructed.
The question of embedding the space of generalized fractional-maximal function in a rearrangementinvariant space is investigated. This question reduces to the embedding of the considered cone in the
corresponding rearrangement-invariant spaces. In addition, conditions for covering a cone generated by
generalized fractional-maximal function by the cone generated by generalized Riesz potentials are given.
Cones from non-increasing rearrangements of generalized potentials were previously considered in the works
of M. Goldman, E. Bakhtigareeva, G. Karshygina and others.
