ON THE BOUNDEDNESS OF THE RIESZ POTENTIAL AND ITS COMMUTATOR’S IN THE GLOBAL MORREY TYPE SPACES WITH VARIABLE EXPONENTS

Onerbek Z.M.
24 June 2022 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2022 #114 Issue 2 53 - 60 pp.

The paper considers the global Morrey-type spaces GM_{p(.),θ(.),w(.)} (Ω) with variable exponents p(.), θ(.), where Ω ⊂ Rⁿ is an unbounded domain. The questions of boundedness of the Riesz potential and its commutator in these spaces are investigated. We give the conditions for variable exponents (formula presented) and on the functions (w₁ (.), w₂ (.)) under which the Riesz potential I^α, will be bounded from (formula presented). The same conditions are obtained for the boundedness of the commutator of the Riesz potential in these spaces. In the case when the exponents p, θ constant numbers, the questions of boundedness of the Riesz potential and its commutator in global Morrey spaces were previously studied by other authors. There are also well-known results on the boundedness of the Riesz potential in global Morrey-type spaces with variable exponents, when the domain Ω ⊂ Rⁿ is bounded.

boundary operator , Morrie-type global spaces , Riess potential , Riesz potential commutator , variable exponent

Text of the article Перейти на текст статьи

Eurasian National University, Nur-Sultan, Kazakhstan

Eurasian National University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026