On boundedness of the generalized B-potential integral operators in the Lorentz spaces
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Ankara Üniversitesi, Türkiye
Dumlupinar Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Integral Transforms and Special Functions (Q3) | ||
| Dergi ISSN | 1065-2469 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2007 |
| Cilt / Sayı / Sayfa | 18 / 12 / 885–895 | DOI | 10.1080/10652460701510980 |
| Özet |
| In this paper, we study the convolution operator (B-convolution), and the generalized B-potential integral and fractional integral (B-fractional integral) with rough kernel, associated with the Laplace-Bessel differential operator Delta(B) = Sigma(k)(i=1) B-i + Sigma(n)(j=k+1)(partial derivative(2)/partial derivative x(j)(2)), B-i = (partial derivative(2)/partial derivative x(i)(2)) + (gamma(i)/x(i))(partial derivative/partial derivative x(i)). We get O'Neil type inequality for the B-convolution. By using O'Neil type inequality we obtain a pointwise rearrangement estimate of the generalized B-potential integral. We prove the boundedness of the generalized B-potential integral operator in the Lorentz spaces, and the proof is based on the pointwise estimate of the rearrangement of this operator. |
| Anahtar Kelimeler |
| B-fractional integral | Generalized B-potential integrals | Laplace-Bessel differential operator | Lorentz spaces | O'Neil type inequality |