Cones generated by a generalized fractional maximal function

0575313 - MÚ 2024 RIV KZ eng J - Článek v odborném periodiku
Bokayev, N. A. - Gogatishvili, Amiran - Abek, A. N.
Cones generated by a generalized fractional maximal function.
Bulletin of the Karaganda University. Mathematics Series. Roč. 110, č. 2 (2023), s. 53-62. ISSN 2518-7929
Institucionální podpora: RVO:67985840
Klíčová slova: cones generated by generalized fractional-maximal function * covering of cones * non-increasing rearrangements of functions
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://dx.doi.org/10.31489/2023M2/53-62

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 rearrangement-invariant 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.
Trvalý link: https://hdl.handle.net/11104/0345097