| Yazarlar |
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi |
Javanshir J. Hasanov
|
| Özet |
| We consider the generalized shift operator, associated with the Laplace-Bessel differential operator Delta(B) = Sigma(n)(i=1) partial derivative(2)/partial derivative x(i)(2) + Sigma(k)(i=1) gamma(i)/x(i) partial derivative/partial derivative x(i). The maximal operator M-gamma (B-maximal operator) and the Riesz potential I-gamma(alpha) (B-Riesz potential), associated with the generalized shift operator are investigated. At first, we prove that the B-maximal operator M-gamma is bounded from the B-Morrey space L-p,L-lambda,L-gamma to L-p,L-lambda,L-gamma for all 1 < p < infinity and 0 <= lambda < n + vertical bar gamma vertical bar. We prove that the B-Riesz potential I-gamma(alpha), 0 < alpha < vertical bar gamma vertical bar is bounded from the B-Morrey space L-p,L-lambda,L-gamma to L-q,L-lambda,L-gamma if and only if alpha/(n+vertical bar gamma vertical bar - lambda) = 1/p - 1/q, 1 < p < (n + vertical bar gamma vertical bar - lambda)/alpha. Also we prove that the B-Riesz potential I-gamma(alpha) is bounded from the B-Morrey space L-1,L-lambda,L-gamma to the weak B-Morrey space WLq,lambda,gamma if and only if alpha/(n + vertical bar gamma vertical bar - lambda) = 1 - 1/q. |
| Anahtar Kelimeler |
| B-maximal operator | B-Morrey space | B-Riesz potential | Hardy-Littlewood-Sobolev-Morrey type estimate |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
| Dergi ISSN | 0022-247X |
| Dergi Grubu | Q1 |
| Makale Dili | İngilizce |
| Basım Tarihi | 11-2008 |
| Cilt No | 347 |
| Sayı | 1 |
| Sayfalar | 113 / 122 |
| Doi Numarası | 10.1016/j.jmaa.2008.03.077 |
