Cones generated by a generalized fractional maximal function

Authors

  • N.А. Bokayev
  • A. Gogatishvili
  • А.N. Abek

DOI:

https://doi.org/10.31489/2023m2/53-62

Keywords:

rearrangement-invariant spaces, non-increasing rearrangements of functions, cones generated by generalized fractional-maximal function, covering of cones

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.

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Published

2023-06-30

Issue

Section

MATHEMATICS