ON THE BOUNDEDNESS OF A GENERALIZED FRACTIONAL-MAXIMAL OPERATOR IN LORENTZ SPACES
Abek А.N. Turgumbayev M.Zh. Suleimenova Z.R.
30 June 2023al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2023#118Issue 23 - 10 pp.
In this paper considers a generalized fractional-maximal operator, a special case of which is the classical fractional-maximal function. Conditions for the function Φ, which defines a generalized fractional-maximal function, and for the weight functions w and v, which determine the weighted Lorentz spaces Λp (v) and Λq (w) (1 < p ≤ q < ∞) under which the generalized maximal-fractional operator is bounded from one Lorentz space Λp (v) to another Lorentz space Λq (w) are obtained. For the classical fractional maximal operator and the classical maximal Hardy-Littlewood function such results were previously known. When proving the main result, we make essential use of an estimate for a nonincreasing rearrangement of a generalized fractional-maximal operator. In addition, we introduce a supremal operator for which conditions of boundedness in weighted Lebesgue spaces are obtained. This result is also essentially used in the proof of the main theorem.
fractional-maximal function , generalized fractional-maximal operator , non-increasing rearrangement , supremal operator , weighted Lorentz spaces
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L.N. Gumilyov Eurasian national university, Astana, Kazakhstan
Karaganda University named after Academician E.A. Buketov, Karaganda, Kazakhstan
L.N. Gumilyov Eurasian national university
Karaganda University named after Academician E.A. Buketov
10 лет помогаем публиковать статьи Международный издатель
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