The Stein-Weiss type inequalities for the B-Riesz potentials
Yazarlar (4)
Akif Gadjıev
Prof. Dr. Vagıf GULIYEV Kütahya Dumlupınar Üniversitesi
Ayhan Şerbetçi Ankara Üniversitesi, Türkiye
Emin V. Gulıyev
| Makale Türü | Özgün Makale (Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale) | ||
| Dergi Adı | J. Math. Inequal. | ||
| Dergi ISSN | 1846-579X Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | MathSciNet | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2011 |
| Cilt / Sayı / Sayfa | 5 / 1 / 87–106 | DOI | – |
| 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. |
| Anahtar Kelimeler |