| Yazarlar |
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi |
Rza Ch. Mustafayev
|
|
Ayhan Serbetci
|
| 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 |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | COMPLEX VARIABLES AND ELLIPTIC EQUATIONS |
| Dergi ISSN | 1747-6933 |
| Dergi Grubu | Q3 |
| Makale Dili | İngilizce |
| Basım Tarihi | 01-2010 |
| Cilt No | 55 |
| Sayı | 8 |
| Sayfalar | 847 / 863 |
| Doi Numarası | 10.1080/17476930902999074 |
