Cylindrical Critical Hardy Type Inequalities and Identities

Shaimerdenov Y. Yessirkegenov N.
June 2025 Springer

Journal of Mathematical Sciences (United States)
2025 #291 Issue 1 135 - 147 pp.

We investigate the critical case of a weighted cylindrical Hardy inequality involving a logarithmic term and extend the classical result due to Edmunds and Triebel to this case: For functions in C0∞Rnx′=0 we establish the sharp inequality ‖fx′N/21+logx′β/2‖L2≤21-β‖x′∙∇Nfx′N/21+logx′β/2‖L2 where x = (x′, x′′) ∈ ℝ^N ×ℝ^n−N, 1 ≤ N ≤ n, and β ∈ℝ. We obtain improved versions of this inequality with remainder terms and discuss their nonattainability. As an application, we derive a family of Caffarelli–Kohn–Nirenberg type and uncertainty type inequalities.

Text of the article Перейти на текст статьи

SDU University, 1/1 Abylai Khan St., Kaskelen, Almaty, 040900, Kazakhstan
Ghent University, 281, Krijgslaan, Building S8, Ghent, B 9000, Belgium
Institute of Mathematics and Mathematical Modeling, 125, Pushkin St, Almaty, 050010, Kazakhstan
KIMEP University, 2, Abay Av, Almaty, 050010, Kazakhstan

SDU University
Ghent University
Institute of Mathematics and Mathematical Modeling
KIMEP University

10 лет помогаем публиковать статьи Международный издатель

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