Stein-Weiss inequalities for the fractional integral operators in Carnot groups and applications
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Rza Ch. Mustafayev Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Ayhan Serbetci Ankara Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Complex Variables and Elliptic Equations (Q3) | ||
| Dergi ISSN | 1747-6933 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2010 |
| Cilt / Sayı / Sayfa | 55 / 8 / 847–863 | DOI | 10.1080/17476930902999074 |
| Makale Linki | https://www.tandfonline.com/doi/abs/10.1080/17476930902999074 | ||
| Özet |
| In this article we consider the fractional integral operator I α on any Carnot group 𝔾 (i.e. nilpotent stratified Lie group) in the weighted Lebesgue spaces L p,ρ(x)β (𝔾). We establish Stein–Weiss inequalities for I α, and obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional integral operator I α from the spaces L p,ρ(x)β (𝔾) to L q,ρ(x)−γ (𝔾), and from the spaces L 1,ρ(x)β (𝔾) to the weak spaces WL q,ρ(x)−γ (𝔾) by using the Stein–Weiss inequalities. In the limiting case , we prove that the modified fractional integral operator is bounded from the space L p,ρ(x)β (𝔾) to the weighted bounded mean oscillation (BMO) space BMOρ(x)−γ (𝔾), where Q is the … |
| Anahtar Kelimeler |
| Fractional integral operator | Stein-Weiss inequality | Stratified groups | Weighted BMO spaces | Weighted Lebesgue spaces |
| Atıf Sayıları | |
| Google Scholar | 21 |
| Web of Science | 9 |