THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS
Yazarlar (4)
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Ankara Üniversitesi, Türkiye
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Journal of Mathematical Inequalities (Q1) | ||
| Dergi ISSN | 1846-579X Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 03-2011 |
| Cilt / Sayı / Sayfa | 5 / 1 / 87–106 | DOI | 10.7153/jmi-05-09 |
| 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 |
| Atıf Sayıları | |
| WoS | 6 |
| SCOPUS | 12 |
| Google Scholar | 20 |