Email this article Hardy—Steklov operators and Sobolev-type embedding inequalities
- Authors: Nasyrova M.G.1, Ushakova E.P.2
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Affiliations:
- Computing Center
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 293, No 1 (2016)
- Pages: 228-254
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/173770
- DOI: https://doi.org/10.1134/S0081543816040179
- ID: 173770
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Abstract
We characterize weighted inequalities corresponding to the embedding of a class of absolutely continuous functions into a fractional-order Sobolev space. As auxiliary results of the paper, which are also of independent interest, we obtain several new types of necessary and sufficient conditions for the boundedness of the Hardy–Steklov operator (integral operator with two variable limits) in weighted Lebesgue spaces.
About the authors
M. G. Nasyrova
Computing Center
Author for correspondence.
Email: nassm@mail.ru
Russian Federation, ul. Kim Yu Chena 65, Khabarovsk, 680000
E. P. Ushakova
Steklov Mathematical Institute of Russian Academy of Sciences
Email: nassm@mail.ru
Russian Federation, ul. Gubkina 8, Moscow, 119991
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