Cones of monotone function generated by a generalized fractional maximal function

0585978 - MÚ 2025 RIV TR eng J - Journal Article
Bokayev, N. A. - Gogatishvili, Amiran - Abek, A. N.
Cones of monotone function generated by a generalized fractional maximal function.
TWMS Journal of Pure and Applied Mathematics. Roč. 15, č. 1 (2024), s. 127-141. ISSN 2076-2585. E-ISSN 2219-1259
R&D Projects: GA ČR(CZ) GA23-04720S
Institutional support: RVO:67985840
Keywords : re-arrangement function * invariant spaces * maximal function * function spaces
OECD category: Pure mathematics
Impact factor: 3.8, year: 2022
Method of publishing: Limited access
https://doi.org/10.30546/2219-1259.15.1.2024.2487

In this paper, we consider the generalized fractional maximal function and use it to introduce the space of generalized fractional maximal functions and the various cones of monotone functions generated by generalized fractional maximal functions MΦf. We introduced three function classes. We give equivalent descriptions of such cones when the function Φ belongs to some function classes. The conditions for their mutual covering are given. Then, these cones are used to construct a criterion for embedding the space of generalized fractional maximal functions into the re-arrangement invariant spaces (RIS). The optimal RIS for such embedding is also described.
Permanent Link: https://hdl.handle.net/11104/0353604