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
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
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 |
| Özet |
| In this article we consider the fractional integral operator I-alpha on any Carnot group G (i. e. nilpotent stratified Lie group) in the weighted Lebesgue spaces L-p,L- rho(x)beta (G). We establish Stein-Weiss inequalities for I-alpha, and obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional integral operator I-alpha from the spaces L-p,L- rho(x)beta (G) to L-q,L- rho(x)-gamma (G), and from the spaces L-1,L- rho(x)beta (G) to the weak spaces WLq, rho(x)-gamma (G) by using the Stein-Weiss inequalities. In the limiting case p = Q/alpha-beta-gamma, we prove that the modified fractional integral operator (I) over tilde (alpha) is bounded from the space L-p,L- rho(x)beta (G) to the weighted bounded mean oscillation (BMO) space BMO (rho(x)-gamma) (G), where Q is the homogeneous dimension of G. As applications of the properties of the fundamental solution of sub-Laplacian L on G, we prove two Sobolev-Stein embedding theorems on weighted Lebesgue and weighted Besov spaces in the Carnot group setting. As another application, we prove the boundedness of I-alpha from the weighted Besov spaces B-p theta,beta(s) (G) to B-q theta, - gamma(s)(G). |
| Anahtar Kelimeler |
| Fractional integral operator | Stein-Weiss inequality | Stratified groups | Weighted BMO spaces | Weighted Lebesgue spaces |