Necessary and sufficient conditions for the boundedness of B-Riesz potential in the B-Morrey spaces
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
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 Analysis and Applications (Q1) | ||
| Dergi ISSN | 0022-247X Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 11-2008 |
| Cilt / Sayı / Sayfa | 347 / 1 / 113–122 | DOI | 10.1016/j.jmaa.2008.03.077 |
| 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 |