Cones generated by a generalized fractional maximal function
Жалпыланған бөлшектi-максималды функциямен туындаған конустар
Конусы, порожденные обобщенной дробно-максимальной функцией
Bokayev N.А. Gogatishvili A. Abek A.N.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 253 - 62 pp.
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. All rights reserved
cones generated by generalized fractional-maximal function , covering of cones , non-increasing rearrangements of functions , rearrangement-invariant spaces
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Institute of Mathematics, The Czech Academy of Sciences, Prague, Czech Republic
L.N. Gumilyov Eurasian National University
Institute of Mathematics
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