| Yazarlar (4) |
A. D. Gadjiev
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan |
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye |
|
A. Serbetci
Ankara Üniversitesi, Türkiye |
|
E. V. Guliyev
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan |
| Özet |
| We establish two inequalities of Stein-Weiss type for the Riesz potential operator I-alpha,I-gamma (B-Riesz potential operator) generated by the Laplace-Bessel differential operator Delta B in the weighted Lebesgue spaces L-p,L-vertical bar x vertical bar beta,L-gamma. We obtain necessary and sufficient conditions on the parameters for the boundedness of Ia,. from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to L-q,L-vertical bar x vertical bar-lambda,L-gamma, and from the spaces L-1,L-vertical bar x vertical bar beta,L-gamma to the weak spaces WLq,vertical bar x vertical bar-lambda,gamma. In the limiting case p = Q/alpha we prove that the modified B-Riesz potential operator (I) over tilde (alpha,gamma) is bounded from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to the weighted B-BMO spaces BMO vertical bar x vertical bar-lambda,gamma. As applications, we get the boundedness of I-alpha,I-gamma from the weighted B-Besov spaces B-p theta,vertical bar x vertical bar beta,gamma(s) to the spaces B-q theta,vertical bar x vertical bar-lambda,gamma(s). Furthermore, we prove two Sobolev embedding theorems on weighted Lebesgue L-p,L-vertical bar x vertical bar beta,L-gamma and weighted B-Besov spaces B-p theta,vertical bar x vertical bar beta,gamma(s) by using the fundamental solution of the B-elliptic equation Delta(alpha/2)(B) |
| Anahtar Kelimeler |
| B-Riesz potential | Laplace-Bessel differential operator | Stein-weiss type inequalities | Weighted B-Besov space | Weighted lebesgue space |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale |
| Dergi Adı | JOURNAL OF MATHEMATICAL INEQUALITIES |
| Dergi ISSN | 1846-579X Wos Dergi Scopus Dergi |
| Dergi Grubu | Q1 |
| Makale Dili | İngilizce |
| Basım Tarihi | 03-2011 |
| Cilt No | 5 |
| Sayı | 1 |
| Sayfalar | 87 / 106 |
| Doi Numarası | 10.7153/jmi-05-09 |
| Atıf Sayıları | |
| WoS | 6 |
| SCOPUS | 12 |
| Google Scholar | 20 |
